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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