## Problem 147

**Forum rules**

As your posts will be visible to the general public you

are requested to be thoughtful in not posting anything

that might explicitly give away how to solve a particular problem.

This forum is NOT meant to discuss solution methods for a problem.

In particular don't post any code fragments or results.

Don't start begging others to give partial answers to problems

Don't ask for hints how to solve a problem

Don't start a new topic for a problem if there already exists one

Don't start begging others to give partial answers to problems

Don't ask for hints how to solve a problem

Don't start a new topic for a problem if there already exists one

See also the topics:

Don't post any spoilers

Comments, questions and clarifications about PE problems.

### Problem 147

Hi,

Are there 1120 different rectangles that can be situated in a 5x7 grid?

Thanks!

Are there 1120 different rectangles that can be situated in a 5x7 grid?

Thanks!

"think(O(n))+O(n) sometimes is better than think(O(1))+O(1)"

### Re: Problem 147

I get 420 for a 5*7 grid, but I'm not so sure about my answer.

Math and Programming are complements

### Re: Problem 147

Oh, I mean vertical + horizontal + cross-hatched rectangles, but I've verified it using brute force.

Thanks for the time!

Thanks for the time!

Last edited by axelbrz on Mon Nov 10, 2008 8:14 am, edited 1 time in total.

"think(O(n))+O(n) sometimes is better than think(O(1))+O(1)"

### Re: Problem 147

I'm trying to solve it but I haven't found any algorithm to find the number of cross hatched ones yet

Math and Programming are complements

### Re: Problem 147

Lol, try to see the cross-hatched grid as a normal matrix

Good luck!

Good luck!

"think(O(n))+O(n) sometimes is better than think(O(1))+O(1)"

### Re: Problem 147

The question is a little ambiguous. Do you mean only in a strictly 5x7 grid or in that size grid and ALL smaller ones as required in the problem???axelbrz wrote:Are there 1120 different rectangles that can be situated in a 5x7 grid?

When you assume something, you risk being wrong half the time.

### Re: Problem 147

No, no, I was referring in a strictly 5x7 grid, but I've resolved the problem, I had a trivial mistake in the program when I asked that.

So, thanks too!

So, thanks too!

"think(O(n))+O(n) sometimes is better than think(O(1))+O(1)"

### Problem 147

Hi,

Can anyone confirm if these rectangles are correct. This is assuming just strictly that rectangle, so 3x2 is just 37.

3x3 = 87

3x4 = 56

3x5 = 209

4x4 = 264

4x5 = 395

2x12 = 343

2x13 = 392

1x20 = 229

10x9 = 7660

10x10 = 9502

Thanks for your help.

**Problem 147**(View Problem)Can anyone confirm if these rectangles are correct. This is assuming just strictly that rectangle, so 3x2 is just 37.

3x3 = 87

3x4 = 56

3x5 = 209

4x4 = 264

4x5 = 395

2x12 = 343

2x13 = 392

1x20 = 229

10x9 = 7660

10x10 = 9502

Thanks for your help.

### Re: Problem 147

3x3 is correct, the rest is not.

Here something is obviously wrong, as the latter contains at least all the rectangles of the former.lg5293 wrote:3x3 = 87

3x4 = 56

_{Jaap's Puzzle Page}

### Re: Problem 147

I hope it's not too much to emphasize that the result for a 5 by 7 grid is NOT 1120.

### Re: Problem 147

I have difficulty understanding the conditions in this question.

First when considering the second set of 35 rectangles contained within the horizontal-vertical rectangles, surely you are double counting, not only the smaller grids themselves, but also their contents, so they aren't different.

Also for example the 2x2 grid contains 4 1x1 horizontal-vertical rectangles as well as 2x1's and 1x2's which themselves can be re-cross-hatched and double counted as above to contain yet more rectangles. Where do you stop? Does the question imply a limit to the reduction of contained horizontal-vertical rectangles?

First when considering the second set of 35 rectangles contained within the horizontal-vertical rectangles, surely you are double counting, not only the smaller grids themselves, but also their contents, so they aren't different.

Also for example the 2x2 grid contains 4 1x1 horizontal-vertical rectangles as well as 2x1's and 1x2's which themselves can be re-cross-hatched and double counted as above to contain yet more rectangles. Where do you stop? Does the question imply a limit to the reduction of contained horizontal-vertical rectangles?

### Re: Problem 147

They are not sub-grids of each other. The question just asks you to examine one grid of each possible size up to some maximum size limit, and add their results together.

_{Jaap's Puzzle Page}

### Re: Problem 147

Not sub-grids, ok. I now realise how I misread the question. Thanks for the clarification.