Friday, August 20, 2010

Friday Puzzle (Hard): 1105

Let's finish off two weeks of puzzles with some challenging math and a more gentle riddle.  First, the math:

The sum of the squares of two consecutive numbers is 1105.

What are the numbers?

3 comments:

Joshua Fahey said...

23 & 24

Eye of the Frog said...

Seems Joshua beat me, so the best I can do is show the work. I kinda have to since I was called out in the most recent post. :)


x^2 + (x+1)^2 = 1105
x^2 + x^2 + 2x + 1 = 1105
2x^2 + 2x = 1104
x^2 + x = 552
x^2 + x + .25 = 552.25
(x+.5)^2 = 552.25
x + .5 = 23.5
x = 23

I did miss the bicycle riddle and the "what's special about this number" riddle. Straight math like this is a bit easier for me. :)

Thomas L. McDonald said...

I think I have the smartest readers on the planet.

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