Is this a shortcut?

useless · Long-term Member

Is this a shortcut?

bradp · Senior Member

I would do it like this:

start with 4900 (70*70)

for the OI of foil/loif, it's 70(4) + 70(1) which is really just 70(5), so 4900+350 = 5250

now add 1*4 to get 5254

that formula might be good if you have it memorized, but foiling is just as effective

Date: Jun 7, 2006

A. From algebra we learn:

(10a + b) (10a + (5-b)) =

1. 100(a2 + a/2) + 10(0) + b(5-b), if a is even

2. 100(a2 + a-1/2) + 10(5) + b(5-b), if a is odd

B. Using numbers instead of variables we get the following:

1. Multiply the one's digits. Write this down.

2. If a is even, write 0. If a is odd, write 5.

3. If a is even, add a/2 to a2. Write this value down.

4. If a is odd, add a-1/2 to a2. Write this value down.

C. Examples:

Ex [1] 41 x 44 = ______

a. Multiply 1 x 4 = 4. Write down 4.

b. Since a=4 is even, write 0.

c. Add 42 + 4/2 = 18. Write 18.

d. The answer is 1804.

useless · Long-term Member

Excellent solution! THAT ROCKS TO THE MAX!!! Thanks!

However, I think on the odds, I think you meant to say a^2 + (a/2 - 1/2) for the thousands and hundreds digits, right?

Thanks again for the shortcut. I was on the right track, I just didnt think about it that way.

- Zack -

useless · Long-term Member

Oh wait, it was: (a-1)/2.

I'm an idiot. >_<

Sorry.

-Zack -

fht · Long-term Member

Just foil it, what's wrong with foiling?

Plus, though I acknowledge it's a valid way to do a problem, I don't think it shortens the thinking process that much. If you foil fast, there's no need to remember 2 extra solutions.

bradp · Senior Member

I'm going to show up at a meet next year wrapped in aluminum foil.

Date: Jun 7, 2006

Dude, that's an awesome idea!!!!!!!!!!!!

fht · Long-term Member

Show them how proud we are being foilers, ha.

useless · Long-term Member

If we all make it to state... I say we all do that. It'll be hilarious, and I know that White will at least crack a smile. Its usually such a stressful atmosphere... why not make it a little more bearable?

Anyway, I dont think that its too hard of a trick to remember. Its just like the numbers that end in 5's trick, which is pretty fast if you have that practiced. I should practice foiling more. I still need to move faster.

- Zack -