# The lost number

The Chinese are incredible with the numbers, although somehow it seems that they do everything backwards, like their writing. They seem to do the sums by subtracting and the divisions multiplying. They are very good at mental arithmetic and make strange calculations through rules or tricks that they cannot or do not want to explain.

One of his teachers taught me some exercises of additions that, in his peculiar Chinese way, he invested to do them by subtraction and working from back to front from the answer to obtain the figures that were added.

He asked me to order the nine numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 and any other number that I chose in a sum of two rows, to add them and then delete both addends and one of the numbers of the result and that he would rebuild it. On the board you can see what was left after following his instructions.

Although the real puzzle is simply to say what is the mysterious figure Could you put the missing 10 digits again?

#### Solution

As all the figures added give 45, whose figures add up to 9. We know that the sum of any combination of these figures used only once, must be equal to 9. Given that 1 +? + 1 + 3 + 4 + 1 = 10, the closest number whose numbers add up to 9 is 18, so we know that 8 (18-10) is the mysterious figure.