Given a rectangular table, two players take turns in laying quarters one at a ti

Question

Given a rectangular table, two players take turns in laying quarters one at a time on its surface. Any two coins can touch but cannot overlap. The player placing the last coin on the table is the winner. The player putting the first coin has a winning strategy. What is it? Consider a similar game with a spherical ball. Two players take turns in placing congruent spherical caps on the ball so they will smoothly touch the ball. Any two caps can touch but not overlap. The player placing the last cap on the ball is the winner. Who has the winning strategy now?

Explanation / Answer

The winning strategy is as follows

The first player puts first quarter right in the middle of the centre.

Now wherever the second player puts the quarter the first player puts a quarter in a position directly opposite to the second players' quarter w.r.t. center of the board. This is always possible. As for any position the second player's quarter occupies its opposite position will be unoccupied before the first player makes his move.

Hence this is the winnign strategy.

The same strategy works here as with quarters. And first player has winning strategy

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