A puzzle for the mathletes

[pokerfan]

A large, square, brick wall is one brick higher and one brick narrower than another wall. How many more bricks are in the first wall?

[suninvited]

1. They are both square? nt

[pokerfan]

2. one wall is 'one brick higher and one brick narrower'

[suninvited]

3. Wouldn't they be equal.

I am no mathlete, thats for sure.

[pokerfan]

4. nope

(but very close)

[suninvited]

5. youre gonna make me get out the graph paper.

having never been a great math student, I still find I can solve a lot of math problems with graph paper.

[pokerfan]

14. graph paper will get you there

4x4=16; 3x5=15
5x5=25; 4x6=24
6x6=36; 5x7=35
7x7=49; 6x9=48
8x8=64; 7x9=63
9x9=81; 8x10=80
10x10=100; 9x11=99
11x11=121; 10x12=120
12x12=144; 11x13=143

I first noticed this when I was memorizing multiplication tables back in third grade.

Anyway, this will be in Marilyn's column in Parade magazine this Sunday.

[KitchenWitch]

6. Zero

[JVS]

7. one

Let's just say that our big square is ten bricks high and ten long, for a total of 100. The other wall is only 9 bricks high but 11 bricks wide for 99.

[JVS]

8. We can try it again for a wall that is 12x12

it is 144, one lower but wider is 13x11= 143, one less

[JVS]

10. Let us generalize the form

Our square wall is always x bricks long and high for a total of x^2 bricks.

The wall it surpasses is always (x-1)*(x+1) bricks = x^2-1

It will always be one brick smaller

[suninvited]

9. youre right and it works for any size

I had just figured it out, but you beat me to it.

I was using 9x9 opposed to 10x8.

Way to go.

[JVS]

11. See number 10, I generalized it

[pokerfan]

12. check out the big brain on JVS

[suninvited]

13. no kidding

he must have a giant head to hold all that.