2010 Regional

[jholland]

Does anyone know of a short way of working #51 144^2 - (89)(233) ?

[My#SenseIsTingling]

If you look at some of the UIL's from this year you can see Mr. White has been going with a trick of a square minus the product of two numbers which equals 1 or -1.

For instance,
34^2-(21)(55) = ________ is 1.

He's used the
n^2 - (a)(b) = 1 format all year.

I would have just squared the 4, equal to 6 and subtracted the 3x9 = 7.
6 - 7 = -1

I know I'm not explaining fully, but he's used it a few times this year. You just have to notice that the ones that look hard in the third column, aren't as hard as you think. Hope this helps.

[Toojdwin]

Notice that these problems are always of the form (F)^2 - (F)(F) where F is the nth Fibonacci number. If n is even, it equals -1, and if n is odd, it equals 1. However, it's quicker to just do the first digit thing.

[tiredmathcoach]

Looking for a quick way to do #71: 1(1!)+2(2!)+3(3!)+...+6(6!)=

#46: is their a great shortcut for 2/3 - 101/149

[hansond10]