pythagoras123
  • pythagoras123
Peter and Jane take turns subtracting perfect squares from a given whole number and the person who subtracts the last number to get zero is the winner. If the whole number is 29, and Peter is the first player. what perfect number must he subtract in order for him to definitely win?
Mathematics
schrodinger
  • schrodinger
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experimentX
  • experimentX
16 then Jane would have to subtract either 4 or 9, then jackpot for Peter
pythagoras123
  • pythagoras123
Er.. But Jane can subtract 1 and 16 also..
experimentX
  • experimentX
Yeah ... it seems that way.

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experimentX
  • experimentX
29 = 25 + 4 = 16 + 9 + 4 but there's no other way. If Jane subtracts 1 ... then it would ruin game.
pythagoras123
  • pythagoras123
29= 16+1+9+1+1+1 Jane would then draw the last one
asnaseer
  • asnaseer
It might be best here to work in reverse. i.e. write down the outcome if, after your turn, Jane was left with 1, 2, 3, etc
asnaseer
  • asnaseer
you can then build up to a point where you can work out your best move
experimentX
  • experimentX
the other way seem to be 16+4+1+1+1+1+1+1+1+1+1 and 16+1+1+1+1+1+1+1+1+1+1+1+1+1 for Peter to win, I don't think peter will win if jane does not cooperate.
asnaseer
  • asnaseer
here is the table I worked out so far: after Peter moves, if he leaves: 1 => Jane wins 2 => Jane wins 3 => Peter wins 4 => Jane wins 5 => Jane wins 6 => Peter wins 7 => Jane wins 8 => Jane wins 9 => Jane wins 10 => Jane wins 11 => Peter wins 12 => Jane wins 13 => Peter wins so, as experimentX suggested, if Peter takes 16 first, that will leave 13 which means he would win.
experimentX
  • experimentX
it seems rather like game of odd - even

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