dominoes and chess

I am posting this puzzle for two reasons: It is one of my favorites and I would like to check if Lee, who likes such a challenge, is still reading this blog ...
But of course everybody is invited to post an answer.

We consider a chessboard (8x8 squares) and 32 dominoes. The dominoes are of such size that they cover exactly two squares on the chess board.
But now assume that we cut off two squares at diagonally opposite corners of the chess board and take away one of the dominoes.
Is it possible to put the remaining 31 dominoes on the board so that all of the remaining 62 squares are covered and if yes how?

10 comments:

Anonymous said...

No. I won't say more because I too hope Lee is still reading your blog.

wolfgang said...

Of course there can be many reasons why somebody would stop reading this blog ... but I hope he will still respond.
Btw the mutilated chessboard is a classic with its own wikipedia page and the first time I saw it was at Martin Gardner's page in Sci. Am.

Lee said...

Wolfgang,
I'm still here and plan to continue to be here. I check to see if you've written anything new or have posted a new music video most days, although not all. Ed beat me to your last brain teaser but thanks for posting it anyway. Btw, I'm selfish and want you to continue to post at least occasionally on this blog because I get a great deal of enjoyment from it. More often would be better from my perspective.

I think I've seen this brain teaser before, but I don't remember the answer. I'll think about it some and if I come up with something I'll let you know even if someone beats me to it. I suspect anonymous knows the answer already.

Lee

wolfgang said...

Lee,

good to see you.
I was only worried a bit because I did not see you here or at CIP's place in a while ...

Lee said...

There may be a way to cover the squares with the tiles, but I can't find it if there is. Intuitively it seems to me that if you can cover them on an 8 by 8 board one should be able to do the same thing on a 2 by 2 board. However, if you remove the diagonal corners on a 2 by 2 board you can see right away that it is impossible to cover the remaining 2 squares with the tile. Maybe it is different with an 8 by 8 board, but I don't understand why it necessarily should be.

I still read CIP's blog but I was becoming so repetitive in my comments that I decided it would be best to stop commenting for a while and see if I had any fresh thoughts. It's fun to comment if in doing so one is refining one's own ideas, but to just keep saying the same thing with no refinement is boring for me and is certainly boring for anybody who reads them.

I really do appreciate you, and Ed too, for posting on your blogs. Over a large number of years now they have provided me with considerable enjoyment. I think there are still a few good blogs available, but none has provided me with nearly as much enjoyment and made me think as much as this blog and Ed's blog.

wolfgang said...

Lee,

I don't want to spoil the fun of finding things out, but if you do get tired, the solution is at the link I posted with my first comment.

>> as much as this blog and Ed's blog
Thank you very much, but I think Scott, Cosma, Lubos (about physics), John and several others write much better stuff obviously.

wolfgang said...

And speaking of Martin Gardner, I really like his opinion that "I don't know" is in several cases the best possible answer.

CapitalistImperialistPig said...

Lee - I like your comments, even if they sometimes make me crotchety. You don't let me get away with much.

CapitalistImperialistPig said...

Lee, PS, slight hint, (skip if you prefer)
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Look at 3x3

CapitalistImperialistPig said...

Oops, never mind