MathDB

We have a set of

343

closed jars, each containing blue, yellow and red marbles with the number of marbles from each color being at least

1

and at most

7

. No two jars have exactly the same contents. Initially all jars are with the caps up. To flip a jar will mean to change its position from cap-up to cap-down or vice versa. It is allowed to choose a triple of positive integers

(b; y; r) \in \{1; 2; ...; 7\}^3

and flip all the jars whose number of blue, yellow and red marbles differ by not more than

1

from

b, y, r

, respectively. After

n

moves all the jars turned out to be with the caps down. Find the number of all possible values of

n

, if

n \le 2021

Problem Statement