2017 Combinatorics #3: Nice man depositing coins
Source:
February 19, 2017
Problem Statement
There are jars in a row on a table, initially empty. Each day, a nice man picks ten consecutive jars and deposits one coin in each of the ten jars. Later, Kelvin the Frog comes back to see that of the jars all contain the same positive integer number of coins (i.e. there is an integer such that of the jars have exactly coins). What is the maximum possible value of ?