Math Is Fun Forum

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

3 keys are needed

HI

http://i764.photobucket.com/albums/xx28 … azy/ww.jpg

You can only pick 3 keys that will open the tunnels and allow you to go from one room to the next. The keys are shown on top and are 1,2,3,4,5,6,7
To go through a tunnel you need two keys (the entrance one and the other at
the end of the tunnel.)

Example:
To travel from the top left room to the room underneath it you need keys (1,3) or (7,5) etc. To travel horizontally from the upper left you need keys (6,5),(2,7), etc.
You must start in the upper left corner and finish at the bottom right corner. You can move up,down right, left as long as you have the keys.

Last edited by bobbym (2009-09-12 17:54:31)

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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.

dol88

Member

Registered: 2009-03-15

Posts: 6

Re: 3 keys are needed

Needed keys: 2,3,4

Moves: Down, Down, Right, Up, Right, Down

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: 3 keys are needed

Hi Bobby,

Same answer as dol88.

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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: 3 keys are needed

Hi;

Can you prove that is the only solution?

---

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: 3 keys are needed

Hi Bobby,

Can you prove that is the only solution?

Only graphically, showing that other options deadend. I can't think of any other way.

Last edited by phrontister (2009-09-13 06:44:01)

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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: 3 keys are needed

Hi phrontister;

I did it the mule way.

---

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: 3 keys are needed

You might have to enlighten this donkey, Bobby

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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: 3 keys are needed

Hi phrontister;

It was explained to me that there is a difference between a donkey, a mule and a burro. Don't worry, I forgot what it was. This has no point but I just wanted to say it. I did this:

Last edited by bobbym (2009-09-13 06:15:34)

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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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 3 keys are needed

You missed some:

267
345
367
467

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Why did the vector cross the road?
It wanted to be normal.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: 3 keys are needed

Hi mathsyperson;

I didn't miss them, I wanted the biggest prime of the form 2^n -1 < 35, so I ignored them.

Last edited by bobbym (2009-09-13 06:49:42)

---

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: 3 keys are needed

Hi Bobby,

I kept my tests down to these:

I wanted the biggest square of the form n² < 36, so if there were any other valid combinations that I could have ignored I would have.

Last edited by phrontister (2009-09-13 08:06:22)

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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: 3 keys are needed

Hi;

Thats less. But why did you knock out 251 going right without testing.

If the dude that posed this problem had increased this to say 5 by 5 it would have made it much more difficult to get at.

---

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: 3 keys are needed

But why did you knock out 251 going right without testing.

I didn't actually reject it as such...I never considered it, as there was no need to. I chose combinations that went right quite independently of those that went down.

Going right from the first box I chose the 2-key combinations 65, 27, 45 & 76, while going down I chose 21, 75, 13 & 23. The third keys for those combinations were chosen from adjacent tunnels (ahead) that contained one key from the first tunnel.

With 251 there's no entrance and exit key combination going right that contains two of those digits...but going down there is.

If the dude that posed this problem had increased this to say 5 by 5 it would have made it much more difficult to get at

That dude must be a gentle-hearted soul oozing with barrel-loads of consideration for others.

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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

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: 3 keys are needed

Or maybe creating a bigger puzzle would have been much harder for him.

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Why did the vector cross the road?
It wanted to be normal.

phrontister

Real Member

From: The Land of Tomorrow

Registered: 2009-07-12

Posts: 4,818

Re: 3 keys are needed

Yes...I sense that he is struggling with the deep concepts of this puzzle.

Last edited by phrontister (2009-09-13 12:39:50)

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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