Sunday Times Teaser 2674 – Roll Model
by Peter G Chamberlain
I have a board game with squares numbered 1 to 100 on which moves are determined by throwing two dice, one ten sided and numbered 1 to 10, the other four sided and numbered with four primes.
A move consists of throwing the two dice, choosing the the number on either dice or their sum, and then moving forwards or backwards by this number of squares.
After landing on one square, I realised that there were only two squares that could not be reached by any of the possible scores on my next move. Both were prime numbers not on the four sided die.
(a) Which square was I on?
(b) What are the numbers on the four sided die?