This is a solution to the sum to fifteen two player game puzzle.
A short description of the puzzle:
Two players alternately pick numbers from $1,2,3,\dots, 9$. The first one to pick some three numbers which sum to 15 is the winner. Does anyone have a winning strategy?
This puzzle is basically two people playing tic-tac-toe!
Look at this magic square (image swiped from wikipedia):
Each row, column and diagonal sum to 15.
Also notice that all the even numbers are at the corners.
If you pick three numbers, only one (or three) of which appear at a corner, then the sum is even and cannot be 15.
If you pick three numbers, none or two of which are at the corners, then you have to pick a whole row/column/diagonal to make the sum 15.
So, the sum to fifteen puzzle is basically playing tic-tac-toe, which has no winning strategy for either player.
A short description of the puzzle:
Two players alternately pick numbers from $1,2,3,\dots, 9$. The first one to pick some three numbers which sum to 15 is the winner. Does anyone have a winning strategy?
Solution
This puzzle is basically two people playing tic-tac-toe!
Look at this magic square (image swiped from wikipedia):
Each row, column and diagonal sum to 15.
Also notice that all the even numbers are at the corners.
If you pick three numbers, only one (or three) of which appear at a corner, then the sum is even and cannot be 15.
If you pick three numbers, none or two of which are at the corners, then you have to pick a whole row/column/diagonal to make the sum 15.
So, the sum to fifteen puzzle is basically playing tic-tac-toe, which has no winning strategy for either player.
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