## Two Pieces of Paper

A forum for good logic/math puzzles.

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kandalf
Posts: 41
Joined: Tue Jun 03, 2008 1:16 am UTC

### Two Pieces of Paper

Please note I did not come up with this puzzle, and the solution is available on the web - please refrain from looking it up and posting it here - solve it yourself!

I was presented with this problem this summer, and I enjoyed it a lot. I don't think it's too difficult.

And the original puzzle title is a hint, so I've put it in spoiler tags, use it if you'd like:
Spoiler:
Sixteen Blocks

Have fun!

hnooch
Posts: 128
Joined: Mon Nov 26, 2007 6:55 pm UTC

### Re: Two Pieces of Paper

I just got well and truly sniped. Well done.
Spoiler:
The two lists with crossed out words, along with the hint, suggest a boggle game between two extremely skilled players. Finding out the number of blocks for each letter wasn't too bad; finding the locations was a lot worse. A long analysis finally yielded:

Code: Select all

`A A T ON T S PS O E SW E R I`

Or, any rotation or reflection. I'm pretty sure it's consistent with all the words listed. One place I might have gone astray: I assumed N did not touch P because there were no words sharing those two letters consecutively; however, I also can't think of any words off the top of my head with that arrangement, so I guess it's not necessary to separate them. I'm not sure if my solution is unique. (again, up to rotation and reflection)

Cauchy
Posts: 602
Joined: Wed Mar 28, 2007 1:43 pm UTC

### Re: Two Pieces of Paper

hnooch wrote:I just got well and truly sniped. Well done.
Spoiler:
The two lists with crossed out words, along with the hint, suggest a boggle game between two extremely skilled players. Finding out the number of blocks for each letter wasn't too bad; finding the locations was a lot worse. A long analysis finally yielded:

Code: Select all

`A A T ON T S PS O E SW E R I`

Or, any rotation or reflection. I'm pretty sure it's consistent with all the words listed. One place I might have gone astray: I assumed N did not touch P because there were no words sharing those two letters consecutively; however, I also can't think of any words off the top of my head with that arrangement, so I guess it's not necessary to separate them. I'm not sure if my solution is unique. (again, up to rotation and reflection)

Spoiler:
It doesn't matter whether you rotate or reflect the board, because the ANSWER IS POTATOES.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
Thanks, skeptical scientist, for knowing symbols and giving them to me.

hnooch
Posts: 128
Joined: Mon Nov 26, 2007 6:55 pm UTC

### Re: Two Pieces of Paper

Cauchy wrote:
Spoiler:
It doesn't matter whether you rotate or reflect the board, because the ANSWER IS POTATOES.

Other than the fact that
Spoiler:
"potatoes" is a word that can be found on that boggle board and which neither of the two players found,
I don't see how that's relevant, much less the answer. Enlighten?

fyjham
Posts: 240
Joined: Wed Nov 21, 2007 1:16 am UTC

### Re: Two Pieces of Paper

hnooch wrote:
Cauchy wrote:Other than the fact that
Spoiler:
"potatoes" is a word that can be found on that boggle board and which neither of the two players found,
I don't see how that's relevant, much less the answer. Enlighten?

Here's the reason...
Spoiler:
Follow the board you wrote in a spiral, you can get the whole phrase "AnswerIsPotatoes".

No chance I'd have ever seen that without yours and cauchy's replies though.

kandalf
Posts: 41
Joined: Tue Jun 03, 2008 1:16 am UTC

### Re: Two Pieces of Paper

Spoiler:
potatoes, that is. I spent a while before figuring out it was boggle, and I was able to use some educated guessing to go from there.

Well done!

Dave Rapp
Posts: 79
Joined: Sun Mar 23, 2008 6:57 am UTC
Location: Illinois
Contact:

### Re: Two Pieces of Paper

Wow.

Having never played boggle and having no idea how it is played, I had no idea where to begin. I need to stop coming to topics like this.
My webcomic is made with 100% LEGO products and I think you should check it out.
http://www.lq-comic.com

kandalf
Posts: 41
Joined: Tue Jun 03, 2008 1:16 am UTC

### Re: Two Pieces of Paper

Technically it can be done without a knowledge of boggle - an analysis of the duplicates of letters shows that there are only sixteen letters making up all the words, and then it's just an anagram. Made easier if you guess the first bit.