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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Comments
First comment! That was a really smart and thoughtful teaser! I love using logic.
Thanks for posting it up!
Thanks for posting it up!
I'm way into math, so this was easy. Good show!
good
I remember having to find (and prove) that pattern in college.
As a math person, it was easy. Nice teaser! Math is all about patterns!!!
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