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Omni-MATH / We have two piles with 2000 and 2017 coins respectively.

Problem

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

problem

We have two piles with 20002000 and 20172017 coins respectively. Ann and Bob take alternate turns making the following moves: The player whose turn is to move picks a pile with at least two coins, removes from that pile tt coins for some 2≤t≤42\le t \le 4, and adds to the other pile 11 coin. The players can choose a different tt at each turn, and the player who cannot make a move loses. If Ann plays first determine which player has a winning strategy.
Plain-text mathematical notation (without MathML)
We have two piles with 2000 and 2017 coins respectively. 
Ann and Bob take alternate turns making the following moves: 
The player whose turn is to move picks a pile with at least two coins, removes from that pile t coins for some 2≤t≤4, and adds to the other pile 1 coin. The players can choose a different t at each turn, and the player who cannot make a move loses. 
If Ann plays first determine which player has a winning strategy.
Original LaTeX notation
We have two piles with $2000$ and $2017$ coins respectively. 
Ann and Bob take alternate turns making the following moves: 
The player whose turn is to move picks a pile with at least two coins, removes from that pile $t$ coins for some $2\le  t \le 4$, and adds to the other pile $1$ coin. The players can choose a different $t$ at each turn, and the player who cannot make a move loses. 
If Ann plays first determine which player has a winning strategy.

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Source and history

task_id
f4c98847-60bb-5bce-94c7-3e49c9da57b4
task_key
test--f4c98847-60bb-5bce-94c7-3e49c9da57b4
task_revision_id
1
config / split
/ test

Official source

initial import