Enigma 1386: Fair shares
7 October 2013
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From New Scientist #2546, 8th April 2006
It was Penny’s birthday and Joe provided a box of 25 sweets. He arranged five saucers in a circle and placed 5, 1, 9, 2 and 8 sweets in that order round the circle in the saucers.
To share out the sweets Penny and her four friends had to take turns to remove sweets from or replace sweets in a saucer of their choice until there were five sweets in each. Any sweets removed were placed temporarily on the table.
However, Joe stipulated that if they moved a number of sweets into or out of a saucer, then they must move the same number of sweets into or out of the two adjacent saucers. So each turn consisted of three moves. Needless to say they tried to share out the sweets as quickly as possible.
What is the minimum number of turns needed to share out the sweets?
Penny and Joe are revisited in Enigma 1410.