Enigma 1556: Card trick
5 March 2012
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From New Scientist #2719, 1st August 2009 [link]
Joe gave Penny a rectangular piece of card 12 centimetres by 6 centimetres with the instruction that she had to draw four straight lines out from the centre of the card to an edge, each a whole number of centimetres long, so that, by cutting along two of the lines, a piece of card with an area equal to any multiple of 6 square centimetres (from 1 to 6) can be produced.
What will the total length of the four lines be?