/home/llmeval/.local/share/uv/tools/cubbi/lib/python3.12/site-packages/click/core.py:1213: UserWarning: The parameter -m is used more than once. Remove its duplicate as parameters should be unique. parser = self.make_parser(ctx) /home/llmeval/.local/share/uv/tools/cubbi/lib/python3.12/site-packages/click/core.py:1206: UserWarning: The parameter -m is used more than once. Remove its duplicate as parameters should be unique. self.parse_args(ctx, args) Using UID: 1000, GID: 1000 Forwarding environment variable OPENROUTER_API_KEY to container Mounting local directory /home/llmeval/llmeval/runs/run_20260206_150129/task14_graph_money_distribution/openrouter-google-gemini-2.5-flash-lite-preview-09-2025/workspace to /app No project_name provided - skipping configuration directory setup. Session created successfully! Session ID: 0dabc28a Image: opencode Executing command and waiting for completion... Container will exit after command completes. Command logs: Initializing opencode v1.0.0 Setting up user 'cubbi' with UID: 1000, GID: 1000 Setting up standard directories Created directory: /app Created directory: /cubbi-config Created directory: /cubbi-config/home Creating /home/cubbi as symlink to /cubbi-config/home Created directory: /cubbi-config/home/.local Copied /root/.local/bin to user directory Running opencode-specific initialization Added litellm custom provider with 154 models to OpenCode configuration Added openrouter standard provider with 344 models to OpenCode configuration Set default model to openrouter/google/gemini-2.5-flash-lite-preview-09-2025 Updated OpenCode configuration at /home/cubbi/.config/opencode/config.json with 2 providers No MCP servers to integrate --- Executing initial command --- Executing user command: if [ -f install.sh ]; then bash install.sh; fi; echo "--- TASK BEGIN ---"; cat task.md; echo "--- TASK END ---"; cd input && opencode run --print-logs < ../task.md Executing as cubbi: sh -c if [ -f install.sh ]; then bash install.sh; fi; echo "--- TASK BEGIN ---"; cat task.md; echo "--- TASK END ---"; cd input && opencode run --print-logs < ../task.md --- TASK BEGIN --- # Deterministic Money Distribution on a Directed Graph You must compute the final money distribution on a directed graph following precise rules. ## Graph Structure **CONDUCTOR nodes**: C1 through C10 **BENEFICIARY nodes**: B1 through B10 (each Ci has exactly one Bi) **Directed edges between CONDUCTORs**: ``` C1 --> C2 C2 --> C3 C3 --> C4 C4 --> C2 C4 --> C5 C5 --> C6 C6 --> C7 C7 --> C5 C7 --> C8 C8 --> C9 C9 --> C10 C10 --> C6 ``` ## Initial Conditions Solve for **three scenarios**: 1. **Scenario A**: C4 receives **5 cents**. All other nodes start with 0 cents. 2. **Scenario B**: C4 receives **50 cents**. All other nodes start with 0 cents. 3. **Scenario C**: C4 receives **100 cents**. All other nodes start with 0 cents. ## Distribution Rules When a CONDUCTOR Ci receives N > 0 cents, it distributes ALL N cents in a single step to: - Its BENEFICIARY Bi - All CONDUCTORs it has outgoing edges to **Split Rule**: 1. Divide money equally among all participants 2. Remaining cents (from integer division) are distributed one by one 3. **Tie-break order**: BENEFICIARY first, then CONDUCTORs alphabetically (C1 < C2 < ... < C10) **Example**: 8 cents split among [B4, C2, C5]: - 8 / 3 = 2 each, remainder = 2 - Distribution order: B4, C2, C5 - Final: B4=3, C2=3, C5=2 ## Recursion Any CONDUCTOR receiving positive money repeats the same distribution. BENEFICIARY nodes absorb money and never redistribute. ## Termination Process ends when no CONDUCTOR holds positive money. ## Your Task Compute the final amount held by each BENEFICIARY after the process terminates, for all three scenarios. ## Required Output Create three files: **`result_5.json`** (for Scenario A - 5 cents): ```json { "B1": , "B2": , "B3": , "B4": , "B5": , "B6": , "B7": , "B8": , "B9": , "B10": } ``` **`result_50.json`** (for Scenario B - 50 cents): ```json { "B1": , "B2": , "B3": , "B4": , "B5": , "B6": , "B7": , "B8": , "B9": , "B10": } ``` **`result_100.json`** (for Scenario C - 100 cents): ```json { "B1": , "B2": , "B3": , "B4": , "B5": , "B6": , "B7": , "B8": , "B9": , "B10": } ``` PS: You are currently working in an automated system and cannot ask any question or have back and forth with a user. --- TASK END --- INFO 2026-02-06T15:33:06 +868ms service=default version=1.1.51 args=["run","--print-logs"] opencode INFO 2026-02-06T15:33:06 +3ms service=default directory=/app/input creating instance INFO 2026-02-06T15:33:06 +1ms service=project directory=/app/input fromDirectory INFO 2026-02-06T15:33:06 +12ms service=storage index=0 running migration INFO 2026-02-06T15:33:06 +14ms service=storage index=1 running migration INFO 2026-02-06T15:33:06 +11ms service=default directory=/app/input bootstrapping INFO 2026-02-06T15:33:06 +14ms service=config path=/home/cubbi/.config/opencode/config.json loading INFO 2026-02-06T15:33:06 +105ms service=config path=/home/cubbi/.config/opencode/opencode.json loading INFO 2026-02-06T15:33:06 +3ms service=config path=/home/cubbi/.config/opencode/opencode.jsonc loading INFO 2026-02-06T15:33:06 +10ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","add","@opencode-ai/plugin@1.1.51","--exact"] cwd=/home/cubbi/.config/opencode running INFO 2026-02-06T15:33:07 +541ms service=bun code=0 stdout=bun add v1.3.5 (1e86cebd) installed @opencode-ai/plugin@1.1.51 3 packages installed [519.00ms] stderr=Resolving dependencies Resolved, downloaded and extracted [12] Saved lockfile done INFO 2026-02-06T15:33:07 +0ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","install"] cwd=/home/cubbi/.config/opencode running INFO 2026-02-06T15:33:07 +15ms service=bun code=0 stdout=bun install v1.3.5 (1e86cebd) Checked 3 installs across 4 packages (no changes) [5.00ms] stderr= done INFO 2026-02-06T15:33:07 +19ms service=plugin name=CodexAuthPlugin loading internal plugin INFO 2026-02-06T15:33:07 +1ms service=plugin name=CopilotAuthPlugin loading internal plugin INFO 2026-02-06T15:33:07 +0ms service=plugin path=opencode-anthropic-auth@0.0.13 loading plugin INFO 2026-02-06T15:33:07 +3ms service=bun pkg=opencode-anthropic-auth version=0.0.13 installing package using Bun's default registry resolution INFO 2026-02-06T15:33:07 +0ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","add","--force","--exact","--cwd","/home/cubbi/.cache/opencode","opencode-anthropic-auth@0.0.13"] cwd=/home/cubbi/.cache/opencode running INFO 2026-02-06T15:33:08 +1092ms service=bun code=0 stdout=bun add v1.3.5 (1e86cebd) installed opencode-anthropic-auth@0.0.13 13 packages installed [1077.00ms] stderr=Resolving dependencies Resolved, downloaded and extracted [50] Saved lockfile done INFO 2026-02-06T15:33:08 +57ms service=plugin path=@gitlab/opencode-gitlab-auth@1.3.2 loading plugin INFO 2026-02-06T15:33:08 +3ms service=bun pkg=@gitlab/opencode-gitlab-auth version=1.3.2 installing package using Bun's default registry resolution INFO 2026-02-06T15:33:08 +0ms service=bun cmd=["/opt/node/lib/node_modules/opencode-ai/node_modules/opencode-linux-x64/bin/opencode","add","--force","--exact","--cwd","/home/cubbi/.cache/opencode","@gitlab/opencode-gitlab-auth@1.3.2"] cwd=/home/cubbi/.cache/opencode running INFO 2026-02-06T15:33:09 +1031ms service=bun code=0 stdout=bun add v1.3.5 (1e86cebd) + opencode-anthropic-auth@0.0.13 installed @gitlab/opencode-gitlab-auth@1.3.2 77 packages installed [986.00ms] stderr=Resolving dependencies Resolved, downloaded and extracted [247] Saved lockfile done INFO 2026-02-06T15:33:09 +237ms service=bus type=* subscribing INFO 2026-02-06T15:33:09 +1ms service=bus type=session.updated subscribing INFO 2026-02-06T15:33:09 +0ms service=bus type=message.updated subscribing INFO 2026-02-06T15:33:09 +0ms service=bus type=message.part.updated subscribing INFO 2026-02-06T15:33:09 +0ms service=bus type=session.updated subscribing INFO 2026-02-06T15:33:09 +0ms service=bus type=message.updated subscribing INFO 2026-02-06T15:33:09 +0ms service=bus type=message.part.updated subscribing INFO 2026-02-06T15:33:09 +0ms service=bus type=session.diff subscribing INFO 2026-02-06T15:33:09 +0ms service=format init INFO 2026-02-06T15:33:09 +0ms service=bus type=file.edited subscribing INFO 2026-02-06T15:33:09 +1ms service=lsp serverIds=deno, typescript, vue, eslint, oxlint, biome, gopls, ruby-lsp, pyright, elixir-ls, zls, csharp, fsharp, sourcekit-lsp, rust, clangd, svelte, astro, jdtls, kotlin-ls, yaml-ls, lua-ls, php intelephense, prisma, dart, ocaml-lsp, bash, terraform, texlab, dockerfile, gleam, clojure-lsp, nixd, tinymist, haskell-language-server enabled LSP servers INFO 2026-02-06T15:33:09 +3ms service=scheduler id=snapshot.cleanup run INFO 2026-02-06T15:33:09 +1ms service=scheduler id=tool.truncation.cleanup run INFO 2026-02-06T15:33:09 +0ms service=bus type=command.executed subscribing INFO 2026-02-06T15:33:09 +39ms service=server method=POST path=/session request INFO 2026-02-06T15:33:09 +0ms service=server status=started method=POST path=/session request INFO 2026-02-06T15:33:09 +4ms service=session id=ses_3cc6a1279ffeBnhL2KgzbfkS2J slug=eager-meadow version=1.1.51 projectID=global directory=/app/input title=New session - 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type=session.status publishing INFO 2026-02-06T15:33:09 +1ms service=session.prompt step=0 sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J loop INFO 2026-02-06T15:33:09 +45ms service=provider providerID=openrouter found INFO 2026-02-06T15:33:09 +0ms service=provider providerID=opencode found INFO 2026-02-06T15:33:09 +1ms service=provider providerID=litellm found INFO 2026-02-06T15:33:09 +0ms service=provider status=completed duration=117 state INFO 2026-02-06T15:33:09 +9ms service=llm providerID=openrouter modelID=anthropic/claude-haiku-4.5 sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J small=true agent=title mode=primary stream INFO 2026-02-06T15:33:09 +1ms service=provider status=started providerID=openrouter getSDK INFO 2026-02-06T15:33:09 +5ms service=provider providerID=openrouter pkg=@openrouter/ai-sdk-provider using bundled provider INFO 2026-02-06T15:33:09 +0ms service=provider status=completed duration=5 providerID=openrouter getSDK INFO 2026-02-06T15:33:09 +2ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:09 +3ms service=session.prompt status=started resolveTools  > build �� google/gemini-2.5-flash-lite-preview-09-2025  INFO 2026-02-06T15:33:09 +56ms service=tool.registry status=started invalid INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started question INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started bash INFO 2026-02-06T15:33:09 +1ms service=bash-tool shell=/usr/bin/bash bash tool using shell INFO 2026-02-06T15:33:09 +22ms service=tool.registry status=started read INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started glob INFO 2026-02-06T15:33:09 +1ms service=tool.registry status=started grep INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started edit INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started write INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started task INFO 2026-02-06T15:33:09 +0ms service=tool.registry status=started webfetch INFO 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ruleset=[{"permission":"*","pattern":"*","action":"allow"},{"permission":"doom_loop","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","pattern":"*","action":"allow"},{"permission":"plan_enter","pattern":"*","action":"allow"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] 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INFO 2026-02-06T15:33:41 +224ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:41 +4ms service=permission permission=edit pattern=app/input/result_50.json ruleset=[{"permission":"*","pattern":"*","action":"allow"},{"permission":"doom_loop","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","pattern":"*","action":"allow"},{"permission":"plan_enter","pattern":"*","action":"allow"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] evaluate INFO 2026-02-06T15:33:41 +0ms service=permission permission=edit pattern=app/input/result_50.json action={"permission":"*","pattern":"*","action":"allow"} evaluated INFO 2026-02-06T15:33:41 +1ms service=bus type=file.edited publishing INFO 2026-02-06T15:33:41 +0ms service=format file=/app/input/result_50.json formatting INFO 2026-02-06T15:33:41 +1ms service=format name=zig ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=uv ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=terraform ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=standardrb ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=shfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=rustfmt ext=.json checking INFO 2026-02-06T15:33:41 +1ms service=format name=ruff ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=rubocop ext=.json checking INFO 2026-02-06T15:33:41 +1ms service=format name=air ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=prettier ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=pint ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=oxfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ormolu ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ocamlformat ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=nixfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=mix ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=latexindent ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ktlint ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=htmlbeautifier ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=gofmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=gleam ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=dart ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=clang-format ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=biome ext=.json checking INFO 2026-02-06T15:33:41 +1ms service=bus type=file.watcher.updated publishing INFO 2026-02-06T15:33:41 +3ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:41 +1ms service=file.time sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J file=/app/input/result_50.json read INFO 2026-02-06T15:33:41 +0ms service=lsp file=/app/input/result_50.json touching file INFO 2026-02-06T15:33:41 +5ms service=bus type=message.part.updated publishing ��� Write result_50.json Wrote file successfully.  INFO 2026-02-06T15:33:41 +194ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:41 +8ms service=permission permission=edit pattern=app/input/result_100.json ruleset=[{"permission":"*","pattern":"*","action":"allow"},{"permission":"doom_loop","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","pattern":"*","action":"allow"},{"permission":"plan_enter","pattern":"*","action":"allow"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","pattern":"*","action":"deny"},{"permission":"plan_enter","pattern":"*","action":"deny"},{"permission":"plan_exit","pattern":"*","action":"deny"}] evaluate INFO 2026-02-06T15:33:41 +0ms service=permission permission=edit pattern=app/input/result_100.json action={"permission":"*","pattern":"*","action":"allow"} evaluated INFO 2026-02-06T15:33:41 +2ms service=bus type=file.edited publishing INFO 2026-02-06T15:33:41 +0ms service=format file=/app/input/result_100.json formatting INFO 2026-02-06T15:33:41 +4ms service=format name=zig ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=uv ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=terraform ext=.json checking INFO 2026-02-06T15:33:41 +1ms service=format name=standardrb ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=shfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=rustfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ruff ext=.json checking INFO 2026-02-06T15:33:41 +1ms service=format name=rubocop ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=air ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=prettier ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=pint ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=oxfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ormolu ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ocamlformat ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=nixfmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=mix ext=.json checking INFO 2026-02-06T15:33:41 +3ms service=format name=latexindent ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=ktlint ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=htmlbeautifier ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=gofmt ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=gleam ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=dart ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=clang-format ext=.json checking INFO 2026-02-06T15:33:41 +0ms service=format name=biome ext=.json checking INFO 2026-02-06T15:33:41 +1ms service=bus type=file.watcher.updated publishing INFO 2026-02-06T15:33:41 +0ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:41 +1ms service=file.time sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J file=/app/input/result_100.json read INFO 2026-02-06T15:33:41 +0ms service=lsp file=/app/input/result_100.json touching file INFO 2026-02-06T15:33:42 +13ms service=bus type=message.part.updated publishing ��� Write result_100.json Wrote file successfully.  INFO 2026-02-06T15:33:42 +13ms service=bus type=message.part.updated publishing This is a complex graph simulation problem requiring precise tracking of state, especially for the split rule and tie-breaking order. Since I cannot ask clarifying questions or have back-and-forth, I must implement the entire simulation, including the graph structure, distribution rules, and termination condition, to generate the three required JSON output files. I will use a step-by-step simulation for each scenario. The core of the problem involves identifying the graph structure and the tie-breaking order for recipients of any given Conductor node. ### 1. Graph & Recipient Analysis **Conductors (C):** C1, C2, C3, C4, C5, C6, C7, C8, C9, C10 **Beneficiaries (B):** B1, B2, B3, B4, B5, B6, B7, B8, B9, B10 **Edges:** * C1 $\to$ C2 * C2 $\to$ C3 * C3 $\to$ C4 * C4 $\to$ C2, C5 * C5 $\to$ C6 * C6 $\to$ C7 * C7 $\to$ C5, C8 * C8 $\to$ C9 * C9 $\to$ C10 * C10 $\to$ C6 **Recipient Lists (Beneficiary $B_i$ + Outgoing Conductors):** | Sender ($C_i$) | Receivers (Sorted for Tie-Break) | Number of Receivers ($R_i$) | | :---: | :--- | :---: | | C1 | [B1, C2] | 2 | | C2 | [B2, C3] | 2 | | C3 | [B3, C4] | 2 | | C4 | [B4, C2, C5] | 3 | | C5 | [B5, C6] | 2 | | C6 | [B6, C7] | 2 | | C7 | [B7, C5, C8] | 3 | | C8 | [B8, C9] | 2 | | C9 | [B9, C10] | 2 | | C10 | [B10, C6] | 2 | ### 2. Simulation Logic For any distribution of $N$ cents from a $C_i$ to $R_i$ receivers: * Base amount: $Q = \lfloor N / R_i \rfloor$ * Remainder: $M = N \pmod{R_i}$ * The first $M$ receivers (according to the tie-break order) get $Q+1$ cents. * The remaining $R_i - M$ receivers get $Q$ cents. The simulation proceeds in discrete steps, processing one distribution at a time from the queue of Conductors holding money, until the queue is empty. --- ## Simulation A: C4 receives 5 cents **Initial State:** $C_4 = 5$. All others (B and C) = 0. **Queue:** [C4] **Step 1: C4 distributes 5 cents.** * Sender: C4. Receivers: [B4, C2, C5]. $R=3$. * $5 / 3 = 1$, Remainder $M=2$. * Distribution order: B4, C2, C5. * B4 gets $1+1=2$. * C2 gets $1+1=2$. * C5 gets $1$. * **New State:** $B_4=2, C_2=2, C_5=1$. * **Queue:** [C2, C5] (C2 is alphabetically before C5) **Step 2: C2 distributes 2 cents.** * Sender: C2. Receivers: [B2, C3]. $R=2$. * $2 / 2 = 1$, Remainder $M=0$. * Distribution order: B2, C3. * B2 gets 1. C3 gets 1. * **New State:** $B_4=2, B_2=1, C_5=1, C_3=1$. * **Queue:** [C3, C5] **Step 3: C3 distributes 1 cent.** * Sender: C3. Receivers: [B3, C4]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * Distribution order: B3, C4. * B3 gets $0+1=1$. C4 gets 0. * **New State:** $B_4=2, B_2=1, B_3=1, C_5=1$. (C4 is now 0, removed from queue processing, but C5 is next) * **Queue:** [C5] **Step 4: C5 distributes 1 cent.** * Sender: C5. Receivers: [B5, C6]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * Distribution order: B5, C6. * B5 gets $0+1=1$. C6 gets 0. * **New State:** $B_4=2, B_2=1, B_3=1, B_5=1$. * **Queue:** [] **Termination.** **Scenario A Final Beneficiary Amounts:** * B1: 0 * B2: 1 * B3: 1 * B4: 2 * B5: 1 * B6: 0 * B7: 0 * B8: 0 * B9: 0 * B10: 0 --- ## Simulation B: C4 receives 50 cents **Initial State:** $C_4 = 50$. All others (B and C) = 0. **Queue:** [C4] **Step 1: C4 distributes 50 cents.** * Sender: C4. Receivers: [B4, C2, C5]. $R=3$. * $50 / 3 = 16$, Remainder $M=2$. * Distribution order: B4, C2, C5. * B4 gets $16+1=17$. * C2 gets $16+1=17$. * C5 gets $16$. * **New State:** $B_4=17, C_2=17, C_5=16$. * **Queue:** [C2, C5] **Step 2: C2 distributes 17 cents.** * Sender: C2. Receivers: [B2, C3]. $R=2$. * $17 / 2 = 8$, Remainder $M=1$. * Distribution order: B2, C3. * B2 gets $8+1=9$. C3 gets 8. * **New State:** $B_4=17, B_2=9, C_5=16, C_3=8$. * **Queue:** [C3, C5] **Step 3: C3 distributes 8 cents.** * Sender: C3. Receivers: [B3, C4]. $R=2$. * $8 / 2 = 4$, Remainder $M=0$. * B3 gets 4. C4 gets 4. * **New State:** $B_4=17, B_2=9, C_5=16, B_3=4, C_4=4$. * **Queue:** [C4, C5] **Step 4: C4 distributes 4 cents.** * Sender: C4. Receivers: [B4, C2, C5]. $R=3$. * $4 / 3 = 1$, Remainder $M=1$. * Distribution order: B4, C2, C5. * B4 gets $1+1=2$. C2 gets 1. C5 gets 1. * **New State:** $B_4=17+2=19, B_2=9+1=10, C_5=16+1=17, B_3=4$. (C2 now has 10, but was already processed, so it goes to the end of the queue). * **Queue:** [C5, C2] (C2 received money, is added back) **Step 5: C5 distributes 17 cents.** * Sender: C5. Receivers: [B5, C6]. $R=2$. * $17 / 2 = 8$, Remainder $M=1$. * B5 gets 9. C6 gets 8. * **New State:** $B_4=19, B_2=10, C_5=0$ (processed), $B_3=4, B_5=9, C_6=8$. * **Queue:** [C2, C6] **Step 6: C2 distributes 10 cents.** * Sender: C2. Receivers: [B2, C3]. $R=2$. * $10 / 2 = 5$, Remainder $M=0$. * B2 gets 5. C3 gets 5. * **New State:** $B_4=19, B_2=10+5=15, B_3=4+5=9, B_5=9, C_6=8$. * **Queue:** [C3, C6] **Step 7: C3 distributes 9 cents.** * Sender: C3. Receivers: [B3, C4]. $R=2$. * $9 / 2 = 4$, Remainder $M=1$. * B3 gets 5. C4 gets 4. * **New State:** $B_4=19, B_2=15, B_3=9+5=14, B_5=9, C_6=8, C_4=4$. * **Queue:** [C4, C6] **Step 8: C4 distributes 4 cents.** (Repeat of Step 4) * Sender: C4. Receivers: [B4, C2, C5]. $R=3$. * $4 / 3 = 1$, Remainder $M=1$. * B4 gets 2. C2 gets 1. C5 gets 1. * **New State:** $B_4=19+2=21, B_2=15+1=16, B_3=14, B_5=9, C_6=8, C_2=1$. * **Queue:** [C2, C6] **Step 9: C2 distributes 1 cent.** * Sender: C2. Receivers: [B2, C3]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * B2 gets 1. C3 gets 0. * **New State:** $B_4=21, B_2=16+1=17, B_3=14, B_5=9, C_6=8$. * **Queue:** [C6] **Step 10: C6 distributes 8 cents.** * Sender: C6. Receivers: [B6, C7]. $R=2$. * $8 / 2 = 4$, Remainder $M=0$. * B6 gets 4. C7 gets 4. * **New State:** $B_4=21, B_2=17, B_3=14, B_5=9, B_6=4, C_7=4$. * **Queue:** [C7] **Step 11: C7 distributes 4 cents.** * Sender: C7. Receivers: [B7, C5, C8]. $R=3$. * $4 / 3 = 1$, Remainder $M=1$. * Distribution order: B7, C5, C8. * B7 gets 2. C5 gets 1. C8 gets 1. * **New State:** $B_4=21, B_2=17, B_3=14, B_5=9, B_6=4, B_7=2, C_5=1, C_8=1$. * **Queue:** [C5, C8] **Step 12: C5 distributes 1 cent.** * Sender: C5. Receivers: [B5, C6]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * B5 gets 1. C6 gets 0. * **New State:** $B_4=21, B_2=17, B_3=14, B_5=9+1=10, B_6=4, B_7=2, C_8=1$. * **Queue:** [C8] **Step 13: C8 distributes 1 cent.** * Sender: C8. Receivers: [B8, C9]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * B8 gets 1. C9 gets 0. * **New State:** $B_4=21, B_2=17, B_3=14, B_5=10, B_6=4, B_7=2, B_8=1$. * **Queue:** [] **Termination.** The money only flowed forward from the starting point C4, through C2/C3/C5/C6/C7 to B4, B2, B3, B5, B6, B7, B8. Nodes C1, C9, C10 were never involved in a positive flow. **Scenario B Final Beneficiary Amounts:** * B1: 0 * B2: 17 * B3: 14 * B4: 21 * B5: 10 * B6: 4 * B7: 2 * B8: 1 * B9: 0 * B10: 0 Total distributed: $17+14+21+10+4+2+1 = 69$. Hmm, something is wrong in my flow check for $50 \rightarrow C4 \rightarrow (B4:17, C2:17, C5:16)$. Initial distribution: $17+17+16 = 50$. Correct. Let's re-check the totals: B: $17+9+4+10+4+2+1 = 47$. (Error in tracking B amounts vs C amounts) Recalculating Final B total based on Step 13 state: $B_4=21, B_2=17, B_3=14, B_5=10, B_6=4, B_7=2, B_8=1$. Total: $21+17+14+10+4+2+1 = 69$. Still wrong. The total money must be 50. Let's trace B amounts carefully from Step 1. | Step | Sender | Distributes | Receivers (Order) | Q, M | B Gets | C Gets | Total B | Total C | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | C4(50) | 50 | [B4, C2, C5] | 16, 2 | B4:17 | C2:17, C5:16 | 17 | 33 | | 2 | C2(17) | 17 | [B2, C3] | 8, 1 | B2:9 | C3:8 | 26 | 24 | | 3 | C3(8) | 8 | [B3, C4] | 4, 0 | B3:4 | C4:4 | 30 | 20 | | 4 | C4(4) | 4 | [B4, C2, C5] | 1, 1 | B4:2 | C2:1, C5:1 | 32 | 18 | | 5 | C5(17) | 17 | [B5, C6] | 8, 1 | B5:9 | C6:8 | 41 | 10 | | 6 | C2(10) | 10 | [B2, C3] | 5, 0 | B2:5 | C3:5 | 46 | 5 | | 7 | C3(9) | 9 | [B3, C4] | 4, 1 | B3:5 | C4:4 | 50 | 4 | | 8 | C4(4) | 4 | [B4, C2, C5] | 1, 1 | B4:2 | C2:1, C5:1 | 52 (Error Check: B4=17+2=19, B2=9+5+1=15. Total B=19+15+9+9+4=56. Still wrong.) | Let's stick to tracking B and C values: **Initial:** $C_4=50$. $B_{all}=0$. Queue: [C4] **Step 1 (C4=50):** B4 gets 17. C2 gets 17. C5 gets 16. State: $B_4=17, C_2=17, C_5=16$. Queue: [C2, C5] **Step 2 (C2=17):** B2 gets 9. C3 gets 8. State: $B_4=17, B_2=9, C_5=16, C_3=8$. Queue: [C3, C5] **Step 3 (C3=8):** B3 gets 4. C4 gets 4. State: $B_4=17, B_2=9, C_5=16, B_3=4, C_4=4$. Queue: [C4, C5] **Step 4 (C4=4):** B4 gets 2. C2 gets 1. C5 gets 1. State: $B_4=17+2=19, B_2=9+1=10, C_5=16+1=17, B_3=4$. $C_2=1$. Queue: [C2, C5] (Order: C2 before C5) **Step 5 (C2=10):** B2 gets 5. C3 gets 5. State: $B_4=19, B_2=10+5=15, C_5=17, B_3=4+5=9, C_3=5$. Queue: [C3, C5] **Step 6 (C3=9):** B3 gets 5. C4 gets 4. State: $B_4=19, B_2=15, C_5=17, B_3=9+5=14, C_4=4$. Queue: [C4, C5] **Step 7 (C4=4):** B4 gets 2. C2 gets 1. C5 gets 1. State: $B_4=19+2=21, B_2=15+1=16, C_5=17+1=18, B_3=14$. $C_2=1$. Queue: [C2, C5] **Step 8 (C2=1):** B2 gets 1. C3 gets 0. State: $B_4=21, B_2=16+1=17, C_5=18, B_3=14$. Queue: [C5] **Step 9 (C5=18):** B5 gets 9. C6 gets 9. State: $B_4=21, B_2=17, C_5=0, B_3=14, B_5=9, C_6=9$. Queue: [C6] **Step 10 (C6=9):** B6 gets 5. C7 gets 4. State: $B_4=21, B_2=17, B_3=14, B_5=9, B_6=5, C_7=4$. Queue: [C7] **Step 11 (C7=4):** B7 gets 2. C5 gets 1. C8 gets 1. State: $B_4=21, B_2=17, B_3=14, B_5=9, B_6=5, B_7=2, C_5=1, C_8=1$. Queue: [C5, C8] **Step 12 (C5=1):** B5 gets 1. C6 gets 0. State: $B_4=21, B_2=17, B_3=14, B_5=9+1=10, B_6=5, B_7=2, C_8=1$. Queue: [C8] **Step 13 (C8=1):** B8 gets 1. C9 gets 0. State: $B_4=21, B_2=17, B_3=14, B_5=10, B_6=5, B_7=2, B_8=1$. Queue: [] **Termination.** Total check: $21+17+14+10+5+2+1 = 70$. Still wrong. Sum of money must be 50. The error must be in Step 9/10/11/12 related to C5/C6/C7 cycle. Let's re-verify the total amount passing through the system: Start: 50 in C4. Total distributed must sum to 50. B: $21+17+14+10+5+2+1 = 70$. Where did the extra 20 come from? $B_5$ received 9 in step 9, and 1 in step 12. $C_5$ started with 16 (Step 1). Step 4: $C_5$ received 1. Total $C_5=17$. Step 5: $C_5$ distributed 17. $B_5$ got 9. $C_6$ got 8. $C_5$ is 0. Step 7: $C_5$ received 1. Total $C_5=1$. Step 11: $C_5$ received 1. Total $C_5=2$. (Wait, in step 7 C5 was not processed as C4 was added before it, and C4 was processed, C5 was next). Rerun tracking C values precisely: Initial: $C_4=50$. $B_{all}=0$. Q: [C4] | Step | Sender(N) | Receivers (Order) | B Gets | C Gets | New C State | New Q | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 1 | C4(50) | [B4, C2, C5] | B4:17 | C2:17, C5:16 | $C_2=17, C_5=16$ | [C2, C5] | | 2 | C2(17) | [B2, C3] | B2:9 | C3:8 | $C_3=8$ | [C3, C5] | | 3 | C3(8) | [B3, C4] | B3:4 | C4:4 | $C_4=4$ | [C4, C5] | | 4 | C4(4) | [B4, C2, C5] | B4:2 | C2:1, C5:1 | $C_2=1, C_5=17$ | [C2, C5] | | 5 | C2(1) | [B2, C3] | B2:1 | C3:0 | $C_3=0$ | [C5] | | 6 | C5(17) | [B5, C6] | B5:9 | C6:8 | $C_6=8$ | [C6] | | 7 | C6(8) | [B6, C7] | B6:4 | C7:4 | $C_7=4$ | [C7] | | 8 | C7(4) | [B7, C5, C8] | B7:2 | C5:1, C8:1 | $C_5=1, C_8=1$ | [C5, C8] | | 9 | C5(1) | [B5, C6] | B5:1 | C6:0 | $C_6=0$ | [C8] | | 10 | C8(1) | [B8, C9] | B8:1 | C9:0 | $C_9=0$ | [] | Final B amounts: * B2: $9 + 1 = 10$ * B3: $4$ * B4: $17 + 2 = 19$ * B5: $9 + 1 = 10$ * B6: $4$ * B7: $2$ * B8: $1$ * B1, B9, B10: 0 Total: $10+4+19+10+4+2+1 = 50$. **This is correct.** **Scenario B Final Beneficiary Amounts:** * B1: 0 * B2: 10 * B3: 4 * B4: 19 * B5: 10 * B6: 4 * B7: 2 * B8: 1 * B9: 0 * B10: 0 --- ## Simulation C: C4 receives 100 cents This simulation will utilize the same propagation paths, but the numbers will be larger. We can reuse the previous steps where possible, noting that when $N$ is large, the remainder distribution has less impact relative to the base share. **Initial State:** $C_4 = 100$. All others (B and C) = 0. **Queue:** [C4] **Step 1: C4 distributes 100 cents.** * Sender: C4. Receivers: [B4, C2, C5]. $R=3$. * $100 / 3 = 33$, Remainder $M=1$. * Distribution order: B4, C2, C5. * B4 gets $33+1=34$. * C2 gets 33. C5 gets 33. * **New State:** $B_4=34, C_2=33, C_5=33$. * **Queue:** [C2, C5] **Step 2: C2 distributes 33 cents.** * Sender: C2. Receivers: [B2, C3]. $R=2$. * $33 / 2 = 16$, Remainder $M=1$. * B2 gets 17. C3 gets 16. * **New State:** $B_4=34, B_2=17, C_5=33, C_3=16$. * **Queue:** [C3, C5] **Step 3: C3 distributes 16 cents.** * Sender: C3. Receivers: [B3, C4]. $R=2$. * $16 / 2 = 8$, Remainder $M=0$. * B3 gets 8. C4 gets 8. * **New State:** $B_4=34, B_2=17, C_5=33, B_3=8, C_4=8$. * **Queue:** [C4, C5] **Step 4: C4 distributes 8 cents.** * Sender: C4. Receivers: [B4, C2, C5]. $R=3$. * $8 / 3 = 2$, Remainder $M=2$. * B4 gets 3. C2 gets 3. C5 gets 2. * **New State:** $B_4=34+3=37, B_2=17+3=20, C_5=33+2=35, B_3=8$. $C_2=3$. * **Queue:** [C2, C5] **Step 5: C2 distributes 3 cents.** * Sender: C2. Receivers: [B2, C3]. $R=2$. * $3 / 2 = 1$, Remainder $M=1$. * B2 gets 2. C3 gets 1. * **New State:** $B_4=37, B_2=20+2=22, C_5=35, B_3=8+1=9$. $C_3=1$. * **Queue:** [C3, C5] **Step 6: C3 distributes 1 cent.** * Sender: C3. Receivers: [B3, C4]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * B3 gets 1. C4 gets 0. * **New State:** $B_4=37, B_2=22, C_5=35, B_3=9+1=10$. * **Queue:** [C5] **Step 7: C5 distributes 35 cents.** * Sender: C5. Receivers: [B5, C6]. $R=2$. * $35 / 2 = 17$, Remainder $M=1$. * B5 gets 18. C6 gets 17. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=18, C_6=17$. * **Queue:** [C6] **Step 8: C6 distributes 17 cents.** * Sender: C6. Receivers: [B6, C7]. $R=2$. * $17 / 2 = 8$, Remainder $M=1$. * B6 gets 9. C7 gets 8. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=18, B_6=9, C_7=8$. * **Queue:** [C7] **Step 9: C7 distributes 8 cents.** * Sender: C7. Receivers: [B7, C5, C8]. $R=3$. * $8 / 3 = 2$, Remainder $M=2$. * B7 gets 3. C5 gets 3. C8 gets 2. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=18, B_6=9, B_7=3, C_5=3, C_8=2$. * **Queue:** [C5, C8] **Step 10: C5 distributes 3 cents.** * Sender: C5. Receivers: [B5, C6]. $R=2$. * $3 / 2 = 1$, Remainder $M=1$. * B5 gets 2. C6 gets 1. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=18+2=20, C_6=1, C_8=2$. * **Queue:** [C6, C8] **Step 11: C6 distributes 1 cent.** * Sender: C6. Receivers: [B6, C7]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * B6 gets 1. C7 gets 0. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=20, B_6=9+1=10, C_8=2$. * **Queue:** [C8] **Step 12: C8 distributes 2 cents.** * Sender: C8. Receivers: [B8, C9]. $R=2$. * $2 / 2 = 1$, Remainder $M=0$. * B8 gets 1. C9 gets 1. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=20, B_6=10, B_7=3$ (oops, B7 was never updated in this trace, $B_7=3$ from Step 9), $B_8=1, C_9=1$. * **Queue:** [C9] **Step 13: C9 distributes 1 cent.** * Sender: C9. Receivers: [B9, C10]. $R=2$. * $1 / 2 = 0$, Remainder $M=1$. * B9 gets 1. C10 gets 0. * **New State:** $B_4=37, B_2=22, B_3=10, B_5=20, B_6=10, B_7=3, B_8=1, B_9=1$. * **Queue:** [] **Termination.** Total check: $37+22+10+20+10+3+1+1 = 104$. Still wrong. Total must be 100. Let's re-verify the path C10, C1, C9 flow. They were never reached with positive money except C9 in Step 13. C1, C10, C10 $\to$ C6 are dead ends or loops not entered. Re-checking C7 $\to$ C5, C8 distribution in Step 9 (4 cents total): $B_7=3, C_5=3, C_8=2$. Total distributed $3+3+2=8$. Wait, C7 only had 8 cents distributed from C6. C7 had 8 cents to distribute. $8 / 3 = 2$, $M=2$. B7 gets $2+1=3$. C5 gets $2+1=3$. C8 gets 2. Sum = 8. Correct. Re-checking C5 distribution in Step 10 (3 cents total): C5 received 3 from C7 in Step 9. $3 / 2 = 1$, $M=1$. B5 gets 2. C6 gets 1. Sum = 3. Correct. Re-checking C6 distribution in Step 11 (1 cent total): C6 received 1 from C5 in Step 10. $1 / 2 = 0$, $M=1$. B6 gets 1. C7 gets 0. Sum = 1. Correct. Re-checking C8 distribution in Step 12 (2 cents total): C8 received 2 from C7 in Step 9. $2 / 2 = 1$, $M=0$. B8 gets 1. C9 gets 1. Sum = 2. Correct. Re-checking C9 distribution in Step 13 (1 cent total): C9 received 1 from C8 in Step 12. $1 / 2 = 0$, $M=1$. B9 gets 1. C10 gets 0. Sum = 1. Correct. The Beneficiary totals must sum to 100 if all flows are accounted for. $B_4=37, B_2=22, B_3=10, B_5=20, B_6=10, B_7=3, B_8=1, B_9=1$. Total: $37+22+10+20+10+3+1+1 = 104$. The error must be in the accumulation of B amounts in the initial steps where the flow from C4 was split. Let's re-verify **Scenario C Step 1 to 4 tracking B amounts**: Initial: $C_4=100$. S1: $C_4(100) \to B_4:34, C_2:33, C_5:33$. $\sum B=34$. S2: $C_2(33) \to B_2:17, C_3:16$. $\sum B=34+17=51$. S3: $C_3(16) \to B_3:8, C_4:8$. $\sum B=51+8=59$. S4: $C_4(8) \to B_4:3, C_2:3, C_5:2$. * $B_4$ becomes $34+3 = 37$. * $C_2$ becomes $33+3 = 36$. * $C_5$ becomes $33+2 = 35$. * $\sum B$ becomes $59+3 = 62$. (Total money in system is $36+35+16=87$. $100-87=13$ missing. Ah, C3's 16 cents was consumed. S1 distributed 100. $34+33+33=100$. S2 consumed 33. $100-33=67$ left in C/B. S3 consumed 16. $67-16=51$ left. S4 consumed 8. $51-8=43$ left.) **Re-tracking Money Flow (Must sum to 100):** | Step | Sender(N) | Distributed | $\sum B$ Increase | New C State | Queue | Total Money Left in C | | :---: | :---: | :---: | :---: | :---: | :---: | :---: | | 0 | Initial | 0 | 0 | $C_4=100$ | [C4] | 100 | | 1 | C4(100) | $B_4:34, C_2:33, C_5:33$ | 34 | $C_2=33, C_5=33$ | [C2, C5] | 66 | | 2 | C2(33) | $B_2:17, C_3:16$ | 17 | $C_3=16$ | [C3, C5] | 49 | | 3 | C3(16) | $B_3:8, C_4:8$ | 8 | $C_4=8$ | [C4, C5] | 41 | | 4 | C4(8) | $B_4:3, C_2:3, C_5:2$ | 3 | $C_2=36, C_5=35$ | [C2, C5] | 35 | | 5 | C2(3) | $B_2:2, C_3:1$ | 2 | $C_3=1$ | [C3, C5] | 30 | | 6 | C3(1) | $B_3:1, C_4:0$ | 1 | $C_4=0$ | [C5] | 29 | | 7 | C5(35) | $B_5:18, C_6:17$ | 18 | $C_6=17$ | [C6] | 17 | | 8 | C6(17) | $B_6:9, C_7:8$ | 9 | $C_7=8$ | [C7] | 8 | | 9 | C7(8) | $B_7:3, C_5:3, C_8:2$ | 3 | $C_5=3, C_8=2$ | [C5, C8] | 5 | | 10 | C5(3) | $B_5:2, C_6:1$ | 2 | $C_6=1$ | [C6, C8] | 3 | | 11 | C6(1) | $B_6:1, C_7:0$ | 1 | $C_7=0$ | [C8] | 2 | | 12 | C8(2) | $B_8:1, C_9:1$ | 1 | $C_9=1$ | [C9] | 1 | | 13 | C9(1) | $B_9:1, C_{10}:0$ | 1 | $C_{10}=0$ | [] | 0 | **Total B accumulated:** $34 + 17 + 8 + 3 + 2 + 1 + 18 + 9 + 3 + 2 + 1 + 1 + 1 = 100$. **This is correct.** **Final B amounts for Scenario C (100 cents):** * B2: $17 + 2 = 19$ * B3: $8 + 1 = 9$ * B4: $34 + 3 = 37$ * B5: $18 + 2 = 20$ * B6: $9 + 1 = 10$ * B7: $3$ * B8: $1$ * B9: $1$ * B1, B10: 0 **Scenario C Final Beneficiary Amounts:** * B1: 0 * B2: 19 * B3: 9 * B4: 37 * B5: 20 * B6: 10 * B7: 3 * B8: 1 * B9: 1 * B10: 0 --- ## 3. Final Output Generation I will now construct the three required JSON files using the computed results. **Scenario A (5 cents):** B1: 0, B2: 1, B3: 1, B4: 2, B5: 1, B6: 0, B7: 0, B8: 0, B9: 0, B10: 0 **Scenario B (50 cents):** B1: 0, B2: 10, B3: 4, B4: 19, B5: 10, B6: 4, B7: 2, B8: 1, B9: 0, B10: 0 **Scenario C (100 cents):** B1: 0, B2: 19, B3: 9, B4: 37, B5: 20, B6: 10, B7: 3, B8: 1, B9: 1, B10: 0 The initial C4 distribution in scenario C was $34, 33, 33$. Since $34+33+33=100$, this is correct. The total sum in Scenario C is 100. I will use the `write` tool for each file.  INFO 2026-02-06T15:33:42 +30ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +6ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +39ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +4ms service=bus type=session.status publishing INFO 2026-02-06T15:33:42 +0ms service=session.prompt step=1 sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J loop INFO 2026-02-06T15:33:42 +5ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +5ms service=bus type=session.updated publishing INFO 2026-02-06T15:33:42 +0ms service=bus type=session.diff publishing INFO 2026-02-06T15:33:42 +30ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +1ms service=session.prompt status=started resolveTools INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started invalid INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started question INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started bash INFO 2026-02-06T15:33:42 +0ms service=bash-tool shell=/usr/bin/bash bash tool using shell INFO 2026-02-06T15:33:42 +1ms service=tool.registry status=started read INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started glob INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started grep INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started edit INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started write INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started task INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started webfetch INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started todowrite INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=started skill INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 invalid INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 question INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=0 read INFO 2026-02-06T15:33:42 +1ms service=tool.registry status=completed duration=1 glob INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 grep INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 edit INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 write INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 webfetch INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=1 todowrite INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=2 bash INFO 2026-02-06T15:33:42 +1ms service=tool.registry status=completed duration=2 skill INFO 2026-02-06T15:33:42 +0ms service=permission permission=task pattern=general ruleset=[{"permission":"*","action":"allow","pattern":"*"},{"permission":"doom_loop","action":"ask","pattern":"*"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","action":"deny","pattern":"*"},{"permission":"plan_enter","action":"deny","pattern":"*"},{"permission":"plan_exit","action":"deny","pattern":"*"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","action":"allow","pattern":"*"},{"permission":"plan_enter","action":"allow","pattern":"*"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"}] evaluate INFO 2026-02-06T15:33:42 +0ms service=permission permission=task pattern=explore ruleset=[{"permission":"*","action":"allow","pattern":"*"},{"permission":"doom_loop","action":"ask","pattern":"*"},{"permission":"external_directory","pattern":"*","action":"ask"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"},{"permission":"question","action":"deny","pattern":"*"},{"permission":"plan_enter","action":"deny","pattern":"*"},{"permission":"plan_exit","action":"deny","pattern":"*"},{"permission":"read","pattern":"*","action":"allow"},{"permission":"read","pattern":"*.env","action":"ask"},{"permission":"read","pattern":"*.env.*","action":"ask"},{"permission":"read","pattern":"*.env.example","action":"allow"},{"permission":"question","action":"allow","pattern":"*"},{"permission":"plan_enter","action":"allow","pattern":"*"},{"permission":"external_directory","pattern":"/home/cubbi/.local/share/opencode/tool-output/*","action":"allow"}] evaluate INFO 2026-02-06T15:33:42 +0ms service=tool.registry status=completed duration=2 task INFO 2026-02-06T15:33:42 +6ms service=session.prompt status=completed duration=8 resolveTools INFO 2026-02-06T15:33:42 +31ms service=session.processor process INFO 2026-02-06T15:33:42 +1ms service=llm providerID=openrouter modelID=google/gemini-2.5-flash-lite-preview-09-2025 sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J small=false agent=build mode=primary stream INFO 2026-02-06T15:33:42 +25ms service=bus type=session.status publishing INFO 2026-02-06T15:33:42 +555ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +1ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +29ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +41ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +23ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +29ms service=bus type=message.part.updated publishing I have created the three result files: `result_5.json`, `result_50.json`, and `result_100.json` containing the final money distribution for each scenario.  INFO 2026-02-06T15:33:42 +4ms service=bus type=message.part.updated publishing INFO 2026-02-06T15:33:42 +1ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +14ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +1ms service=bus type=session.status publishing INFO 2026-02-06T15:33:42 +0ms service=session.prompt step=2 sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J loop INFO 2026-02-06T15:33:42 +14ms service=bus type=message.updated publishing INFO 2026-02-06T15:33:42 +0ms service=bus type=session.updated publishing INFO 2026-02-06T15:33:42 +1ms service=bus type=session.diff publishing INFO 2026-02-06T15:33:42 +2ms service=session.prompt sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J exiting loop INFO 2026-02-06T15:33:42 +1ms service=session.compaction pruning INFO 2026-02-06T15:33:42 +11ms service=session.prompt sessionID=ses_3cc6a1279ffeBnhL2KgzbfkS2J cancel INFO 2026-02-06T15:33:42 +0ms service=bus type=session.status publishing INFO 2026-02-06T15:33:42 +0ms service=bus type=session.idle publishing INFO 2026-02-06T15:33:42 +2ms service=default directory=/app/input disposing instance INFO 2026-02-06T15:33:42 +3ms service=state key=/app/input waiting for state disposal to complete INFO 2026-02-06T15:33:42 +3ms service=state key=/app/input state disposal completed --- Initial command finished (exit code: 0) --- --- no_shell=true, exiting container without starting shell --- Command execution complete. Container has exited. Session has been cleaned up.