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4 digit number derived from a single digit (Posted on 2018-02-26)

A number consisting of 2 identical digits, say xx
is multiplied by 99.

Write down the product P, given its tens digit (i.e. 3rd from the left) is y.

P&P only.

No Solution Yet Submitted by Ady TZIDON

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Solution (spoiler)

| Comment 1 of 3

xx*99=(10x+x)*(100-1)=1000x+100x-10x-x=xx00-xx

xx00 - xx = (x, x-1, 10-(x+1), 10-x)

If 10-(x+1)=y => 10-x=y+1; x-1=8-y; x=9-y

P= (9-y,8-y,y,y+1)

Verifying:

99*77: x=7: y=10-(x+1)=2

P= (9-2, 8-2, 2, 2+1) = 7623

Edited on February 26, 2018, 8:42 am

Posted by armando on 2018-02-26 08:41:13

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