Bengt doesn't often play chess. It's not that he doesn't like it, but he gets upset when he loses, and people don't like Bengt when he's upset. So most of his friends don't play with him anymore. But he still likes to make up weird chess problems, usually involving completely unrealistic situations, that would never appear in an actual game. Here's another one:
- What should white do? Bengt can come up with a rather simple solution that leads to mate in four moves, and a more unusual one that leads to mate in only two moves.
- Since Bengt doesn't have anyone to play with, he makes up games and challenges for himself. His latest idea is this: You place a number of white pawns in any of the 16 squares forming one quadrant of the board, let's say the upper left. Then you place a number of black pawns in the quadrant diagonally opposite, in this case the lower right. When you've placed all the pawns, you suspend the board, balancing it on the diagonal between the quadrants, so in this case you lift the lower left and the upper right corner, so the board can pivot around that diagonal. The aim of the game is to get as many more black pawns than white pawns as possible (black pawns minus white pawns should be as big as possible), but so that the board does not tip over to the black side. How many is it possible to get?
Assume that the pawns are pointlike and stand in the middle of the square. You are allowed to use more than one chess set, that it, more than eight of each type of pawn.
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