MathDB

The cells of the

11 \times 111 \times11

cube contain the numbers

1, 2, , . .. . . 1331

, once each number. Two worms are sent from one corner cube to the opposite corner. Each of them can crawl into a cube adjacent to the edge, while the first can crawl if the number in the adjacent cube differs by

8

, the second - if they differ by

9

. Is there such an arrangement of numbers that both worms can get to the opposite corner cube?

Problem Statement