Find the number of ways in which the nine numbers 1,12,123,1234,…,123456789 can be arranged in a row so that adjacent numbers are relatively prime.
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
The six numbers 12,123,12345,123456,12345678, and 123456789 are divisible by 3 , so they cannot be adjacent. However, arranging six numbers in a row with no two adjacent requires at least 11 numbers, which is impossible.
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Source: Omni-MATH,
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