Baltic Way 1996 · Problem 19

Combinatorics

Four heaps contain 38, 45, 61, and 70 matches respectively. Two players take turns choosing any two of the heaps and take some non-zero number of matches from one heap and some non-zero number of matches from the other heap. The player who cannot make a move, loses. Which one of the players has a winning strategy?

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Topics

Games and strategies · Algorithms and processes · Invariants and monovariants

Solutions

Solution

Solution:

The first player wins by making moves so that the opponent must face positions of the form $(a, a, a, b)$ , where $a \leq b$ .

Contest context

Results from Baltic Way 1996

10 teams

Mean score: 5.0 / 5
Scores of 4 or 5: 10 / 10
Estonia: 5 / 5

Score distribution

510

All team scores

Team	Score
Poland	5 / 5
Latvia	5 / 5
Sweden	5 / 5
Denmark	5 / 5
St. Petersburg	5 / 5
Finland	5 / 5
Norway	5 / 5
Lithuania	5 / 5
Estonia	5 / 5
Iceland	5 / 5

Elsewhere

AoPS · Baltic Way 1996
Official results