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A Divisibility Revelation (Posted on 2024-08-28)

14! = 871a82b1200

Without working out 14!, find a and b.

No Solution Yet Submitted by Danish Ahmed Khan

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871a82b1200 must be divisible by both 9 and 11.

The plaintext digits add up to 29, so a+b must be 7 to bring the digital root to be 9.

The plaintext even positions add up to 10, and the odd positions to 19--a difference of 9, which needs to increase to 11.

Revision to the above: a+b must be 7+9=16, rather than 7, as the difference must be even, i.e., 2. They must be 7 and 9.

(a,b) = (7,9).

Edited on August 28, 2024, 11:59 am

Posted by Charlie on 2024-08-28 11:57:46

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