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https://brilliant.org/community-problem … WaLwgLfOIY

How do I approach this problem with M?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

There are 700986 possible rectangles. How did you approach it in your previous favorite language?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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I did not.

I will have to find a way to represent that grid as a martrix first

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

It does seem to lend itself to a visual inspection. How does 84 sound?

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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It sounds like Eihh-tty Fowr. Why does it matter?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

That is the biggest park I have yet and there are 2 of them.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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kind of defeats the whole purpose of 'computer math'. What if it was a much larger matrix?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Then the questioner would not know the answer either.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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That is correct and this is the discussion going on over there:

Finn Hulse, 13 6 days, 7 hours ago

Okay... I just solved this but I forgot which rectangle I found... But pretty much you look for large gaps and then do some counting... Or you could write an immensely complex computer program... But I like my solution. But how is it that as soon as he had posted this problem, it was assigned a rating? How come I can't do that with my problems? Wahh... How do I do the same?

Thaddeus Abiy

Image files are extremely hard to parse,hence the lack of CS solutions..It would have been great if the grid had been provided in a text file or something.

Lokesh Sharma, 18, India 1 day, 14 hours ago

Thought a lot about this problem. Then, eventually I used my old friend MS Paint and got it correct in second shot ^_^

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

That is what I did too but used geogebra, so I did use computer math.

Or you could write an immensely complex computer program... But I like my solution.

Wunderbar Finn Hulse!

Supposing the questioner decided to get tricky and made it 10000 x 10000 and filled in by random the boxes that were blackened, then he would have had to test 2500500025000000 rectangles!

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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bobbym wrote:

Then the questioner would not know the answer either.

so there is no trick?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Hoohohoohohohoho! You sure know how to get at the ole m's vanity. Let me ask you one question, how can a lowly bumpkin like me come up with a trick when those guys could not?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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OK I'll look for a tric but first give me an way to parse the image.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

I would represent the image as a 38 x 43, 2 dimensional array. Putting 0's in the white boxes and 1's in the dark ones.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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I know that already.

How would you convert the image into that array?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Fill the array with zeros first and the label the drawing across the top 1 to 38 and down the side 1 to 43. So A[[1,5]] is the first dark box. A[[3,1]] is the second dark box. A[[3,12]] is the third dark box etc.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Would you assign the black boxes by hand even if there were thousands of them?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

One problem at a time. Why worry about a condition that does not even exist? There is not thousands of blackened boxes. There is just a handful. Always do the minimum amount of work and do not try to generalize for the possibility that there are thousands of boxes.

This goes hand in hand with the Niharika post. Do you remember her problem and my comment about multiple choice questions. You did not follow up on that. You should have because these are all tricks to solving problems in math or even in life. You are allowed to exploit the problem itself to solve it.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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I have solved the problem by asking a 93 year old guy the solution. Does it count?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

You did not answer the problem by asking a 93 year old, you asked me.

Why did you not do what those guys did?

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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That is not horrendous thinking. It is just your viewpoint.

I did not do what those guys did because I gain more pleasure by solving the problem than to just answer it

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

I do not agree and I will keep working on you. In the meantime let us solve this problem before we go asking what would we do if the problem was much larger.

You do not have to enter each darkened box, M has a good matrix editor that would speed the process up.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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OK, I will go to sleep. HAhahhaha!

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,215

Oh okay, if you are tired then get some rest. I will see you when you get up.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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OK I am done

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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