benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Each of the six boxes B₁, B₂, B₃, B₄, B₅, B₆ initially contains one coin. The following operations are allowed Type 1) Choose a non-empty box B_(j), 1≤j≤5, remove one coin from …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Each of the six boxes B1B_1, B2B_2, B3B_3, B4B_4, B5B_5, B6B_6 initially contains one coin. The following operations are allowed Type 1) Choose a non-empty box BjB_j, 1≤j≤51\leq j \leq 5, remove one coin from BjB_j and add two coins to Bj+1B_{j+1}; Type 2) Choose a non-empty box BkB_k, 1≤k≤41\leq k \leq 4, remove one coin from BkB_k and swap the contents (maybe empty) of the boxes Bk+1B_{k+1} and Bk+2B_{k+2}. Determine if there exists a finite sequence of operations of the allowed types, such that the five boxes B1B_1, B2B_2, B3B_3, B4B_4, B5B_5 become empty, while box B6B_6 contains exactly 2010201020102010^{2010^{2010}} coins. [i]
Plain-text mathematical notation (without MathML)
Each of the six boxes B₁, B₂, B₃, B₄, B₅, B₆ initially contains one coin. The following operations are allowed

Type 1) Choose a non-empty box B_(j), 1≤j≤5, remove one coin from B_(j) and add two coins to B_(j+1); 

Type 2) Choose a non-empty box B_(k), 1≤k≤4, remove one coin from B_(k) and swap the contents (maybe empty) of the boxes B_(k+1) and B_(k+2).

Determine if there exists a finite sequence of operations of the allowed types, such that the five boxes B₁, B₂, B₃, B₄, B₅ become empty, while box B₆ contains exactly 2010^(2010²⁰¹⁰) coins.

[i]
Original LaTeX notation
Each of the six boxes $B_1$, $B_2$, $B_3$, $B_4$, $B_5$, $B_6$ initially contains one coin. The following operations are allowed

Type 1) Choose a non-empty box $B_j$, $1\leq j \leq 5$, remove one coin from $B_j$ and add two coins to $B_{j+1}$; 

Type 2) Choose a non-empty box $B_k$, $1\leq k \leq 4$, remove one coin from $B_k$ and swap the contents (maybe empty) of the boxes $B_{k+1}$ and $B_{k+2}$.

Determine if there exists a finite sequence of operations of the allowed types, such that the five boxes $B_1$, $B_2$, $B_3$, $B_4$, $B_5$ become empty, while box $B_6$ contains exactly $2010^{2010^{2010}}$ coins.

[i]

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
872c8dc9-eace-5e0d-b3b1-72342c8ac03c
task_key
test--872c8dc9-eace-5e0d-b3b1-72342c8ac03c
task_revision_id
1
config / split
/ test

Official source

initial import