14 Oct 10
2 edits
Originally posted by AThousandYoungHi 1,000 Young.
The extra square when you slide it the one way is the missing square when you slide it the other way.
[hidden]The missing square is split up among a bunch of other squares which are not true squares in the cut and paste board[/hidden]
No need to hide.
"The missing square is split up among a bunch of other squares which
are not true squares in the cut and paste board."
What 'bunch of other squares.' there is only one square missing.
I think I have done some magic and I'm very clever.
14 Oct 10
Asking about the exact number of squares in the beginning and at the end is a red herring.
Assume that a square on the board is one unit in length, and one in width. Then, the original board has 8*8 units = 64 units squared.
After the cut, the board can be seen as being two 7*8 right triangles, and one 1*8 strip of squares.
(1/2)(7*8) units +(1/2)(7*8) units + (1)(8) units = 64 units squared.
It's just a peculiarity of the slope that our chainsaw artist chose that the board appears to have 'lost' squares. It appears to have lost an intact square, but all the area is still there, and the Universe is still safe.
15 Oct 10
Originally posted by greenpawn34It's not missing. Slide the board the other way to get the missing square - you'll have 65!
Hi 1,000 Young.
No need to hide.
"The missing square is split up among a bunch of other squares which
are not true squares in the cut and paste board."
What 'bunch of other squares.' there is only one square missing.
I think I have done some magic and I'm very clever.
15 Oct 10
Originally posted by greenpawn34If you weigh the two configurations, then you'll see the weight is the same.
Hi
I did this for you guys.
Blog 4
No square is missing.