Let’s think about this simple equation:

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You can immediately see that the calculation is correct. If you take a closer look, you may notice that the same numbers appear to the left and right of the equals sign. The “1” and “2” of the 12 are interchanged in the number 21, but only the numbers that also appear in the result were used in the multiplication. Finally, you might notice that the four-digit number 1260 is the product of two two-digit numbers. This is not an issue of course. Because 1260 = 126 x 10, for example, would also be true.

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Putting all this together gives a definition of the so-called “vampire numbers”. These are natural numbers that can be formed from an even number of digits. It should also be possible to find two factors of a number that each contain half as many digits as the original and together they contain all the digits of the original number (in any order, but they both cannot start or end with ‘0’)..

For example 1260, this means: Since it consists of four numbers, two two-digit numbers, which consist of the numbers 1, 2, 6 and 0, are searched and multiplied together to get 1260 again. It’s easy to convince yourself that only 10, 12, 20, 21 and 60 fit the bill. It immediately follows that only 21 x 60 gives the correct result.