TUYMAADA 2012 S8
- Senior
Integers not divisible by are arranged on the arcs of an oriented graph. We call the weight of a vertexthe difference between the sum of the numbers on the arcs coming into it and the sum of the numbers on the arcs going away from it. It is known that the weight of each vertex is divisible by . Prove that non-zero integers with absolute values not exceeding can be arranged on the arcs of this graph, so that the weight of each vertex is zero.
Proposed by W. Tutte
Dataset text AI-MO AoPS. Quoted with source.
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