Three Heaps, Three Subtractions
Three heaps contain 38, 53 and 71 stones. Two players alternate; a move picks one heap and removes exactly 2, 5 or 6 stones from it (a heap with fewer stones than the amount cannot be used for that amount). A player who cannot move loses. Two moves are different if they use different heaps or different amounts. How many first moves put the opponent in a losing position? Give an integer.
Related problems & prerequisites
Worth solving first
- Nim 3-4-5 6.0/10
- Fibonacci Nim 6.0/10
- Exits from a Wythoff Position 6.0/10
Source: Sprague-Grundy theory applied to a subtraction game; written for AxiomIQ.