Andrej and Barbara play the following game with two strips of newspaper of length $a$ and $b$. They alternately cut from any end of any of the strips a piece of length $d$. The player who cannot cut such a piece loses the game. Andrej allows Barbara to start the game. Find out how the lengths of the strips determine the winner.
Problem
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Tags: game
L567
07.04.2021 16:23
If $a=b$, Andrej copies Barbara and wins, if $a \neq b$, then Barbara cuts the larger piece so that the pieces are now equal. Then, she just copies Andrej and wins @below - Oops, didnt realise that The solution should be this, let $x = \lfloor \frac{a}{d} \rfloor$ and $y = \lfloor \frac{b}{d} \rfloor$. Then, Barbara wins if $x+y$ is odd and Andrej wins otherwise
natmath
07.04.2021 16:25
@above I think $d$ is fixed. Also does 1st grade mean elementary school?
eduD_looC
07.04.2021 16:30
natmath wrote: @above I think $d$ is fixed. Also does 1st grade mean elementary school? Probably not. That's hard core if 1st graders in day school could do this.