Question

Prove that a square can be divided into 1989 squares.

Answer 1

@ajprincess HELP ME Sister.

Answer 2

I spent too much time on this and I'll probably be suspended for spamming now.

Answer 3

ok

Answer 4

Trick: Not all of the 1989 squares are the same size.

Largest square: 59 units by 59 units.

Draw a horizontal and vertical lines one unit from the bottom, and one unit from the right. They can be divided into 59 squares across from bottom. *the corner piece isn't counted twice, additional 58 squares on the side

Each small squares are divided into 4 squares each 1/2 unit by 1/2 unit.

Now - 4 * (58 + 58) = 468 squares.

Divide the large space into 39 by 39 = 1521 squares.

1521 + 468 = 1989 squares

:)

Answer 5

Hint: Not all squares will be of equal size!

Answer 6

ok

Answer 7

Look at the sum of:\[\sum_{x=1}^{n}x ^{2}\] for an appropriate "n" You will see why if you look at the total # of squares in 3x3 and 4x4 to start.

Answer 8

ok

Answer 9

Thank you Sir

Answer 10

So, the key is to find/know/develop the sum for the summation above. Do you know that formula or would you like further help?

Answer 11

btw, you're welcome!

Answer 12

thank you I can calculate it further. Thanks again

Answer 13

Anytime! Nice working with you and good luck in all of your studies! @goformit100 thx for the recognition!

Answer 14

can someone help me on my question ? -- thanks http://openstudy.com/study#/updates/518bd12be4b062a8d1d95949

Answer 15

And you keep on with dividing the top left square into 4. Do this 497 times because 1989 = 1 + (4)(497)