Ms. Arroyo asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Terry ran to her and said, "The sum is 2,500." Ms. Arroyo thought, "Lucky guess," and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Terry was back with the correct answer of 5,625. How does Terry find the sum so quickly?I have a hint and the answer available. If you'd like either, just send me an email, or ask in a comment if I already have your email address. :) Or feel free to tell me how retarded you think these puzzles are. :)
Answer:
The following pattern holds: The sum is equal to n x n, when n is the number of consecutive odd numbers, starting with 1. For example, the sum of the first 3 odd numbers is equal to 3 x 3, or 9; the sum of the first 4 odd numbers is equal to 4 x 4, or 16; the sum of the first 5 odd numbers is equal to 5 x 5, or 25; and so on.
6 comments:
I got it! Take the number of digits you're working with & multiply by 2 (In the first case the result is 100). Then multiply that number by half of the number of digits you're working with (Again in the first case, that's 25). That'll give you the result. FYI, Terry was slow. :D Also, this puzzles rock!
Even if I can't spell "these"...
Morgan:
While your way does work, there's an easier way than that. Mathematically it's equivalent to what you're explaining, but it's much simpler to explain. :)
that kid can multiply well :)
I bet he's good at squaring, too.
this made me think of "series," which made me think of "taylor series" which made me start shaking...but I'm okay now.
Did someone say "squaring"? I think you may be onto something there.
Whoa, I didn't even stop to think of what I was doing (1/2 x 2). Anywho, the answer is just square the number of digits.
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