The cells of the 11×111×11 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? number theorycombinatorics