Enigma 1514: Six a-leaping
25 September 2012
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From New Scientist #2676, 4th October 2008
My family has developed a board game with spaces numbered 0 to 99. A player starts with his counter at 0, throws a die and moves forward the number of spaces shown. If he lands on a space labelled with a square number he jumps forward to the next higher square (for example, if he lands on 49 he jumps to 64). If he lands on a prime number he moves back to the preceding prime number (for example, from 19 he returns to 17), except that from 2 he returns to 0.
If a player throws all six different numbers in turn:
(a) what is the maximum number on the space he can reach?
(b) what is the minimum number on the space that can be reached.