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Ok, so here's a little puzzle I got.

  • I have five different numbers.

  • They all have different amount of digits.

  • If you place them side by side you see the number 32767

How is this even possible!? And more importantly what are the five numbers?

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2 Answers 2

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binary numbers $1, 11, 111, 1111, 11111$, concatenated to yield $$111111111111111_2 = 2^{15} - 1 = 32767$$

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Putting numbers A, B, C, D, and E "side-by-side" results in

the multiplicative expression ABCDE, which is simply the product of the five numbers.

The numbers could be

32767, 20, 0.05, 200000, and 0.000005, which contain 5, 2, 3, 6, and 7 digits, respectively.

Putting them side-by-side yields

(32767)(20)(0.05)(200000)(0.000005) = 32767

With this approach, there are an infinite number of solutions.

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