benchmarks.wiki / Public workspace

Omni-MATH / There are 2017 jars in a row on a table, initially empty. Each day, a nice man…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

There are 2017 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?
Plain-text mathematical notation (without MathML)
There are 2017 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 N of the jars all contain the same positive integer number of coins (i.e. there is an integer d>0 such that N of the jars have exactly d coins). What is the maximum possible value of N?
Original LaTeX notation
There are 2017 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 $N$ of the jars all contain the same positive integer number of coins (i.e. there is an integer $d>0$ such that $N$ of the jars have exactly $d$ coins). What is the maximum possible value of $N$?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

Official source

initial import