Problem #PRU-64568

Problems Methods Examples and counterexamples. Constructive proofs Calculus Number sequences Number sequences (other) Algebraic methods Partitions into pairs and groups; bijections

Problem

Hannah placed 101 counters in a row which had values of 1, 2 and 3 points. It turned out that there was at least one counter between every two one point counters, at least two counters lie between every two two point counters, and at least three counters lie between every two three point counters. How many three point counters could Hannah have?