## 259. Math Puzzle 12/86

We are looking for a specific number that ends in 2. If you move this last digit to the front of the number, the number doubles.

What is the number?
Admittedly, this math puzzle was a bit more challenging than usual. Nevertheless, quite a few readers found the correct solution. Here it is:

Since the number we are looking for doubles when the digit 2 is placed at the beginning, the second-to-last digit can only be 4 $(2 \cdot 2=4)$.

The third-to-last must be 8 $(2 \cdot 4=8)$, and the one before that must be 6 $(8 \cdot 2=16)$. Before that stands a 3 $(1+2 \cdot 6=13)$, and its predecessor is the digit 7 $(1+2 \cdot 3=7)$, and so on.

Since the number we are looking for must start with 1, our calculation process ends as soon as we obtain 10 after doubling a digit and adding the 1 from the tens place of the previously calculated digit.

The number we are looking for is: 105263157894736842

If you continue the process, you will also obtain other numbers that meet our conditions.