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Mathematical cloning brainteaser

By David Shaw, 30 September 2020

Difficulty: Taxing
Grab a calculator (or a pen and paper)
Choose a three-digit number (e.g. 123)
Multiply it by 7
Multiply the answer by 11
Multiply that answer by 13

You will get your starting number written out twice! (e.g. 123 123)
The question is, can you work out why?

Scroll down or click for a hint, or the answer!

Brainteaser hint

What is 7 x 11 x 13? You can use a calculator to help you, if you need it!

Brainteaser answer

Multiplying by 7, 11 and 13 will give you the same answer as if you multiplied by 1001.
7 x 11 x 13 = 1001
And 1001 = 1000 + 1

So if your starting number is 123:
123 x 7 x 11 x 13
= 123 x 1001
= 123 x 1000 + 123 x 1
= 123 000 + 123
= 123 123

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