Here You Go *s*

**SoulAngel** · September 6th, 2005, 04:54 AM

<img src=http://www.geocities.com/reefangel20002000/checker2.gif>

If you were to construct a 6 x 6 checkered square (i.e., a 6 x 6 chess board), how many rectangles would there be in total? You need to include squares too because a square is a special kind of rectangle

"Babe You Get this first up You Eat burnt food for Tea"..smiles [img]graemlins/kiss.gif[/img]

"Rev" ...you get it 1st up I will eat all the topping off Ya pizza" [img]graemlins/pizza.gif[/img]

[ September 06, 2005 01:56 AM: Message edited by: SoulAngel ]

**The Reverend Dark Angel** · September 6th, 2005, 07:15 PM

A whole ******* lot. But the real question is, why would anyone care to find out?

And how'd you know I was eating pizza?

**Draco_High** · September 8th, 2005, 03:52 AM

loads and there is an formula for it......and not saying so I do not get a burnt tea.

If you took the same board and had one grain of rice on the first and two on the second, four on the third how many would you have in the end square?

[ September 07, 2005 12:53 PM: Message edited by: Draco_High ]

**SoulAngel** · September 8th, 2005, 05:48 AM

[i]Thinking there Be only to with Brains to sort this out and there not ganna answer...I dont know the answer....smiles and goes to Find it again laffs and

Rev You always eat pizza when ya not eating something else...

and Draco I know You hate it when I burn Ya Tea.. I seen the dog Eating it the other night.. [img]wink.gif[/img] [img]confused.gif[/img] [i]

**Draco_High** · September 8th, 2005, 08:37 PM

-shoots the dog, skins and butchers.....eats the dog....burps- see dog! how do you like it?

What are Ya talking about Babe? I never over react!!!

[img]graemlins/angel.gif[/img]

**Indea** · October 3rd, 2005, 09:43 AM

sighs ok i will try work this **** out... let me see.......

All the rectangles on the board can be identified by connecting:
2 points of the 7 in the top edge (to form the length of the rectangle) and
2 points of the 7 in the left edge (to form the breadth of the rectangle).

To gain a better understandstanding, consider the 8 x 8 chess board (as soulys pic of the board)
Note that there are 4 possibilities for the lengths of the rectangles to be 5 units.

The following table shows the number of possibilities for different lengths of the rectangles on a 6 x 6 board:

Length of rectangle Number of Possibilities
6 units 1
5 units 2
4 units 3
... ...
1 unit 6

So, number of possibilities for different lengths of rectangles = 1 + 2 + 3 + ... + 6 = 21.
Similarly, number of possibilities for different breadths of rectangles = 1 + 2 + 3 + ... + 6 = 21.
Hence, number of rectangles = 21 x 21 = 441.

Food for thought:

Is there a formula for the sum of the first n positive integers ?
Is 1 + 2 + 3 + 4 + ... + n = n (n + 1) / 2 ?

)

[ October 03, 2005 06:44 AM: Message edited by: Indea ]