Problem #PRU-65054

Problems Methods Examples and counterexamples. Constructive proofs Pigeonhole principle Pigeonhole principle (other)

Problem

The numbers \(1, 2, 3,\dots , 10\) are written around a circle in a particular order. Peter calculated the sum of each of the 10 possible groups of three adjacent numbers around the circle and wrote down the smallest value he had calculated. What is the largest possible value he could have written down?