# The numerical pyramid A numerical pyramid is constructed like the one we see in the figure by placing numbers at the base and placing the sum of two consecutive ones in the top row, in the middle of the previous ones.

What numbers must be placed in the blank boxes to complete the numerical pyramid of the figure?

#### Solution

As each box is filled by adding the lower two, the number that occupies the central box between 6 and 9 intervenes both in the content of the upper right row and in the content of the one on the left. As you have to add both to get 31, it turns out that in 31 intervenes 6, 9 and twice the central square. Thus, as 31 - 6 - 9 = 16, the central box must contain 8. In this way, the two upper boxes will be 6 + 8 = 14 and 9 + 8 = 17. It is easy to verify that 14 + 17 = 31 .

Repeating the process on the other side, 9 + 5 = 14, and since 28 - 14 = 14, which must be twice the central square, the value of this will be 7. Thus, in the immediately superior boxes, it will be 9 + 7 = 16 and 5 + 7 = 12. It is clear that 16 + 12 is 28.

Filling the upper boxes from there is simple.