Shliced numbers

We'll name "Shliced number" a number such as the two first digits build a number multiple of 2, the 3 first digits a number multiple of 3, ... the p first digits a number multiple of p ... up to the full number of N digits multiple of N.
For instance 123654 : 12 multiple of 2, 123 multiple of 3, 1236 multiple of 4, 12365 multiple of 5 and 123654 multiple of 6.

Find all 10 shliced numbers built with ten different digits.
Solution

Find the largest shliced number, without any constraint on digits.
Solution

Find the largest number such as first digit is a multiple of 2, the two first digits build a number multiple of 3, the 3 first digits build a number multiple of 4 etc... up to the full number with n digits, multiple of n+1.
Solution

Details

 

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