Enigma 1110: Dots and lines
19 June 2017
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From New Scientist #2266, 25th November 2000 [link]
Matthew and Ben are playing a game. The board is a 1-kilometre square divided into 1-centimetre squares. The centre of each small square is marked by a red dot.
Matthew begins the game by choosing a number. Ben then selects that number of red dots. Finally Matthew chooses two of Ben’s selected dots and draws a straight line from one to the other. Matthew wins if his line passes through a red dot other than those at its ends; otherwise Ben wins.
What is the smallest number that Matthew can choose to be certain of winning?
In the magazine this puzzle was incorrectly labelled Enigma 1104.