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(472) 6

Part of 1995 Tournament Of Towns

Problems(1)

TOT 472 1995 Autumn J A6 game is played on a 1 x 1000 board

Source:

7/9/2024
A game is played on a 1×10001 \times 1000 board. There are n chips, all of which are initially in a box near the board. Two players move in turn. The first may choose 1717 chips or less, from either on or off the board. She then puts them into unoccupied cells on the board so that there is no more than one chip in each of the cells. The second player may take off the board any number of chips occupying consecutive cells and put them back in the box. The first player wins if she can put all n chips on the board so that they occupy consecutive cells.
(a) Show that she can win if n=98n = 98. (b) For what maximal value of nn can she win?
(A Shapovalov)
combinatorics