There are three sequences that aren't divisible by their last digit: 1234 isn't divisible by 4, 1234567 by 7, or 12345678 by 8. Either replace the last digit in each case with 2, or add 2, and the situation is rectified.

What about the reverse of the 1-9 sequence? 987654321 is divisible by 9, 98765432 by 8, 987654 by 6, 98765 by 5, 9876 by 4, 987 by 3, 98 by 2, 9 by 1. This time only 7 is the snag (as usual) since 9876543 isn't divisible by 7, so we have to add 2 again.

What about dividing the reverse by the last digit? 9 is divisible by 9, 98 isn't divisible by 8, ah but 987 is actually divisible by 7, and the others going downwards are also divisible by their last digit except 987654 isn't divisible by 4. So this time subtract 2 from the odd ones out.

Chris G

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