Math Is Fun Forum

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Squares

Hi,

I found this puzzle on another site.

Place all of the 16 different squares in the 4x4 grid in accordance with the 13 statements below.

#1. The spotted grey square and the spotted blue square are in the same row.
#2. The plain yellow square is directly to the left of the spotted red square.
#3. The plain grey square is directly above the spotted red square.
#4. The plain grey square is directly to the left of the plain white square.
#5. The plain blue square and the spotted grey square are in the same column.
#6. The striped grey square and the plain green square are in same row.
#7. There are two spotted squares and two striped squares in the bottom row.
#8. The spotted blue square and the spotted green square are in the first column.
#9. The top two corners of the grid are occupied by red squares.
#10. The spotted yellow square is in the top row.   
#11. The striped blue square and the striped red square are next to each other in the same row.
#12. The striped yellow square is immediately below the plain green square.
#13. The plain yellow square and the spotted yellow square are in the same column.   

Enjoy!

Last edited by phrontister (2009-12-06 20:46:57)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Squares

Hi phrontister;

This one I am working on and making progress. How long did it take to run the answer off.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Squares

Hi, Bobby,

Took me about an hour to an hour and a half, I think - from working out a strategy to solving it.  I then spent at least that long preparing a graphical solution in case anybody ever asked me about it.

Careful and accurate progress is the key with this type of puzzle - because it's quite long and there are so many statements - and, unlike with some other puzzles, it's hard to backtrack once you discover you've muffed it.

It's so easy to try to speed along, but just as easily you can overlook the tiniest little thing and then you have to start again...which ends up taking so much extra time in the long run.

As with a building project: "Measure twice, cut once".

Last edited by phrontister (2009-12-07 12:37:43)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Squares

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Squares

Hi Bobby,

Yes, that's right.

Here's that graphical solution (in Excel) that I mentioned in post #3.

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Squares

Hi phrontister;

I did it entirely by hand, no computer assistance.

color    Possible boxes

spgre   5,9,13
plblu     5,6,9,12,13,14,16
plgry    7
plwhi    8
stgry    9,12
plyel    10
spred   11
plgre    9,12
spblu    5,9,13
spgry    5,6,9,12,13,14,16
stgre    13,14,15,16
styel     13,16

When I got to this point I couldn't make any more progress with the clues, so I had to guess that styel (striped yellow) was in box 16. Then everything worked out fine. Maybe there was another solution if I made a different choice...

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: Squares

Hi Bobby,

I did it entirely by hand, no computer assistance.

Likewise. I did it on paper (in the same way as in my image) by drawing a grid with R,RD,RS,B,BD,BS,G,GD,GS,Y,YD,YS,A,AD,AS,W ("D" as in "dot" for "spotted" and "A" for grey) down the left-hand side and numbers 1-16 across the top, and dividing those numbers into four groups (as in the image) to represent the grid rows.

I then solved it in the manner typical of this kind of logic puzzle...by putting a cross in the grid boxes where a coloured square couldn't possibly go.

Then, by continually scanning the clues, more crosses are added, to the point where only the solution remains. After solving a clue I crossed out the clue number so I knew not to look at it again...and on the image that is represented by the green squares to the left of the clues.

The image was just my attempt at giving an easy-to-understand way of explaining my strategy. It shows how it can be done neatly (I scribble!) - and on Excel you can also backtrack if you blunder.

Maybe there was another solution if I made a different choice...

The solution is unique, which is confirmed by my strategy.

Last edited by phrontister (2009-12-08 13:16:41)

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"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Squares

Hi phrontister;

The solution is unique, which is confirmed by my strategy

Okay, then. Good work!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ahtivas

Member

Registered: 2010-01-12

Posts: 9

Re: Squares

Here's another puzzle with square.

 http://funmin.com/magic-square.php