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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asked Nov 13, 2020 at 19:38
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2 Answers
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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.
