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A pencil-&-paper nim game
for two


Draw a grid of 6x6=36 squares. The first player - let's say Adam - enters the number '1' in any square. The second (Eve) enters '2' anywhere in the same row or column. Continue in turn - i.e. Adam '3', Eve '4', and so on.

Each new number must be placed in an uninterrupoted rook's move away from its predecessor. 'Uninterrupted' means with no previous number intervening. For example, in the left-hand illustration, Adam could not have played '3' to the left of '1', nor Eve 4 to the north of 2, and Adam cannot play 5 below 3 or above 4.

Play continues until one player loses by having no legal move. The winner scores the value of the last number entered. A player foreseeing defeat may resign, thereby lessening the winner's score. For example, in the completed game (centre), Adam resigned to give Eve a score of 18, as it is obvious that Eve would win with a score of at least 22.

Each subsequent game is started by the loser of the previous one, but starting from the next higher number than the previous score. When the count reaches 36, the cycle is repeated starting from 1 again. The right-hand game was therefore started by Adam at 19. By the time Adam had reached 35, Eve could foresee defeat - but, by playing 36 before resigning, she neatly reduced Adam's potential score of 35 to an actual score of 1!

Copyright © 2017 by David Parlett