MathDB
2017 Combinatorics #3: Nice man depositing coins

Source:

February 19, 2017

Problem Statement

There are 20172017 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 NN of the jars all contain the same positive integer number of coins (i.e. there is an integer d>0d>0 such that NN of the jars have exactly dd coins). What is the maximum possible value of NN?