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 2 years ago
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?
 2 years ago
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?

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experimentX
 2 years ago
Best ResponseYou've already chosen the best response.216 then Jane would have to subtract either 4 or 9, then jackpot for Peter

pythagoras123
 2 years ago
Best ResponseYou've already chosen the best response.0Er.. But Jane can subtract 1 and 16 also..

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2Yeah ... it seems that way.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.229 = 25 + 4 = 16 + 9 + 4 but there's no other way. If Jane subtracts 1 ... then it would ruin game.

pythagoras123
 2 years ago
Best ResponseYou've already chosen the best response.029= 16+1+9+1+1+1 Jane would then draw the last one

asnaseer
 2 years ago
Best ResponseYou've already chosen the best response.1It 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
 2 years ago
Best ResponseYou've already chosen the best response.1you can then build up to a point where you can work out your best move

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.2the 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
 2 years ago
Best ResponseYou've already chosen the best response.1here 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
 2 years ago
Best ResponseYou've already chosen the best response.2it seems rather like game of odd  even
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