perplexus.info :: Numbers : Multiplication Crossed Unknown Digits Muse

Multiplication Crossed Unknown Digits Muse (Posted on 2024-08-09)

Solve;

9999 x ABAD = ABAE1317, where each of the letters A to E represent an integer digit from 0 to 9.

** Computer program assisted solutions are welcome, but semi-analytic (simple calculator and p&p) solutions are preferred.

No Solution Yet Submitted by K Sengupta

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solution

| Comment 1 of 2

The multiplication is plainly

(10,000-1) * ABAD = ABAE1317

10000 * ABAD - ABAD = ABAE1217

The first term ends in 0000

So:

     ... 0000
     -   ____
         1217

Working back from the end (a 3, resulting in a "borrow" producing the needed 7), the four needed digits are 8683.

9999*8683 = 86821317

Assignments of digits:

ABDE
8632

Posted by Charlie on 2024-08-09 11:43:17

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