Enigma 1660: Three dozen
4 December 2011
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From New Scientist #2826, 20th August 2011 [link]
We have been playing our family board game again, where we use a board of 100 spaces numbered 0 to 99. A player starts with his counter on 0, throws a die, and moves forward the number of spaces shown. If he lands on a space marked with a square number he moves forward to the next square number (e.g. if he lands on 49 he jumps to 64). If he lands on a prime he moves back to the preceding prime (e.g. from 19 he returns to 17), except from 2, in which case he returns to 0.
Tom and I played a game. I threw first and moved to a point three times as far up the board as he did. In fact as we continued, my “score” after each throw always remained three times his. After five throws each my score reached 36. The total of all the numbers we had thrown was also 36.
In order, what five numbers did I throw?