perplexus.info :: Numbers : The digit is missing!

The digit is missing! (Posted on 2019-10-14)

Let number N be represented by a chain of 50 “ones”.
The 26th “1”, counting from the right, is replaced by a new digit, say “x”, causing N to become a multiple of 13.
Find x.

No Solution Yet Submitted by Danish Ahmed Khan

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Let us denote by T a number consisting of 6 ones I.e. 111111.

Clearly T is divisible by 1001, and therefore by 13, since 1001=7*11*13.

Our number N can be seen as concatenation TTTTTTx1TTTTTT and its divisibility by 13 is exactly as the divisibility of x1.

x=9 makes x1=91 , a multiple of 13.

Therefore the answer is 9.

P.S. It is a d1 puzzle.

Posted by Ady TZIDON on 2019-10-14 20:25:52

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