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(372) 4

Part of 1993 Tournament Of Towns

Problems(1)

TOT 372 1993 Spring O S4 three piles of stones

Source:

6/10/2024
Three piles of stones are given. One may add to, or remove from one of the piles in one operation the number of stones in the other two piles. For example [12,3,5][12,3,5] can become[12,20,5] [12,20,5] by adding 17=12+517 = 12 + 5 stones to pile 2 or [4,3,5][4,3,5] by removing 8=3+58 = 3 + 5 stones from pile 11. Is it possible starting from the piles with 19931993, 199199 and 1919 stones to get one empty heap after several operations?
(MN Gusarov)
combinatorics