### Brain Teasers

# Below 100

Positive integers form a pyramid. The top row has one number: 1. The second row has three numbers: 2, 3, and 4. The third row has five numbers: 5 through 9, etc.

If the pattern is continued, what number will appear directly below 100?

If the pattern is continued, what number will appear directly below 100?

### Hint

Try to find out the pattern.### Answer

The rightmost number in each row - 1, 4, 9, 16, ... - is a square number, and it's easily seen that the number directly below n^2 is (n+1)^2-1.Therefore, the number directly below 100 (10^2) is 11^2-1=120.

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