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        riddles >> easy >> algebra doodle.
        
(Message started by: Noke Lieu on May 10^th, 2007, 11:52pm)

Title: algebra doodle.
Post by Noke Lieu on May 10^th, 2007, 11:52pm

Thought I'd throw this up before I skip town (again)
came from an algebra doodle from a slow meeting. Nice, and Easy. Lovely.

How to square a 2 digit number:
Take a two digit number. (eg 25)
Round it up to teh nearest ten. (so 30)
Note the difference between the two. (so 5)
Subtract that from the original number (so 20)
Multipy the two numbers together (so 20 x30=600)
Square the difference, then add it. (so 5, 25, 625)
Ta da.

Why should this work?

Will try to pop in, but going to be more remote than I have been over the past few weeks.

Title: Re: algebra doodle.
Post by towr on May 11^th, 2007, 12:55am

[hide]If we take 10a-b
then 10a*(10a-2b)+b² = 100a² -20ab+b² = (10a-b)²
So in particular this is the case if 0 <= b < 10 and 0 < a <= 10
More general take a number a-b, then its square is
a*(a-2b)+b² = a² -2ab+b² = (a-b)²
You can draw this out in a square to give a geometric argument [/hide]

Title: Re: algebra doodle.
Post by Grimbal on May 11^th, 2007, 2:05am

If the units digits is small, you can do it the other way round.

Example: 23
- round down: 20, difference 3.
- add the difference: 23+3 = 26
- multiply: 26*20 = 520
- add the difference squared: 520 + 3² = 529

Title: Re: algebra doodle.
Post by rmsgrey on May 11^th, 2007, 4:56am

It follows trivially from:

[hide](a+b)(a-b)=a²-b²[/hide]

Title: Re: algebra doodle.
Post by ThudanBlunder on May 11^th, 2007, 7:03pm

Title: Re: algebra doodle.
Post by Sameer on May 14^th, 2007, 12:08pm

Reply after a long time... work keeping me busy.. but just to share one square method for numbers ending in 5 is pretty easy...

If you want to square 25 ...

Step 1. Square 5 -> 25
Step 2. Take first digit 2 and multiply it with next digit 3 = 6
Answer 625

Title: Re: algebra doodle.
Post by Grimbal on May 14^th, 2007, 1:29pm

By the way, I participated in a maths contest. One problem involved computing squares of 2-digit numbers. We cannot use calculators. I was so happy to use the trick above.

Title: Re: algebra doodle.
Post by ThudanBlunder on May 14^th, 2007, 1:57pm

on 05/14/07 at 13:29:39, Grimbal wrote:

By the way, I participated in a maths contest. One problem involved computing squares of 2-digit numbers.

When was that? At school? (I trust you spotted my previously attached file of other neat ones.)

Title: Re: algebra doodle.
Post by Grimbal on May 15^th, 2007, 12:45am

Last week-end.

It is the International Contest for Logical and Mathematical Games. It is actually a French contest, but other countries can participate as French regions. Most participants are French-speaking but you start to see other countries from East-Europe. It is mostly for school children and divided by school year, but there are two adult categories, easy and hard.

Yes, I saw your PDF. I haven't had the time to read all the tricks.