Take the first 2 odd numbers, 1 & 3, when you add them up, you get 4. Take the first 3 odd numbers, 1, 3, and 5 when you add them up, you get 9. Now, take the first 5 odd numbers 1, 3, 5, 7, and 9 when you add them together you get 25. Do you see a pattern?
In the brainteaser, Carmen was able to find the sum of the first 50 odd numbers very quickly, her answer was 2500. She did the same for 75 to get 5,625. Do you see the pattern yet?
The pattern is: Instead of adding every single number by hand, you can just square the number of odd numbers (square a number means you multiply a number by itself). For example, the sum of 3 odd numbers = 3 square = 3x3=9; the sum of 5 numbers = 5 square = 5x5= 25. That's why Carmen was able to figure out a number as large as the sum of 75. It's just 75 square which is 75x75 = 5,625.
How cool! HeeHee...I was to lazy to try and figure it out :)
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