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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

Comment 3 of 3 |

P = 121*9*x = 1089 * x

Tens digit (y) from x:

Same as tens digit of 89*x.

But 89*x = (100 - 11) * x and 100*x has zero as tens digit.

So the tens digit is the 9's complement of x, and of course vice versa:

x y

1 8

2 7

3 6

4 5

5 4

6 3

7 2

8 1

9 0

If y is 8, P must be 1089, etc.:

y P

8 1089

7 2178

6 3267

5 4356

4 5445

3 6534

2 7623

1 8712

0 9801

Posted by Charlie on 2018-02-26 12:15:47

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