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rookie1ja

Rabbit Hutch

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Rabbit Hutch - Back to the Matchstick Puzzles

In the picture there are little flats for 6 rabbits. Can you build a dwelling for these 6 rabbits with only 12 matches. Each rabbit must have an equally big space.

Edit: 6 separate flats are needed for the rabbits.

post-2-1175352019_thumbgif

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Rabbit Hutch - solution

Picture added as per below hint.

post-2-1177069379_thumbgif

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All you have to do is make a hexagon and put lines to the center. There, all done!!!

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forgive my rudimentary drawing skills using paint. Each line is a matchstick three triangles split down the middle. Twelve sticks, six pens. yes? no?

Also, there is a way to make six identical rabbit pens using only ten matchsticks. Care to try?

post-402-1181848513_thumbjpg

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What about:

 ---------*---------*

*	*	*	*	*

|	|	|	|	|

|----+----*----+----*

|	|	|	|	|

|	|	|	|	|

 ---------*---------*

Just 11 matches and you also get two guest rooms!

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forgive my rudimentary drawing skills using paint. Each line is a matchstick three triangles split down the middle. Twelve sticks, six pens. yes? no?

Also, there is a way to make six identical rabbit pens using only ten matchsticks. Care to try?

I don't think that works. Some of the matchsticks would end up shorter than the others (the ones splitting the triangles down the middle, I think). So you end up with 9 matchsticks and 3 sticks of a smaller size.

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What about removing the match stick on one side, then joining the two ends together, making a 3D circle with the same hutch design of the original drawing. Is this a legal solution?

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Since there is nothing that says you must have 6 separate flats for the rabbits, this works:

square.gif

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wouldn't this also work (provided my drawing skills... or lack thereof, are excused)?

post-1009-1184622907_thumbjpg

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i know how to use only 6 matches and still use the hexagon form ... cut the matches in half

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Since there are no size requirements, it is possible to do it in 6, (without any cutting in half). But those are going to be some unhappy rabbits.

Rabbit Hutch - solution with 6 sticks

post-1734-1188852463_thumbgif

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Is the answer correct?

Assuming match size is 1,

so original room space is 1/2.

But the new room space is sqrt(3)/4.

Will rabbits be happy?

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Sometimes the wording of these problems are a bit off. Here is another solution that fits in with the wording, though may not be in the spirit of the problem.

post-2143-1191414073_thumbjpg

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Sometimes the wording of these problems are a bit off. Here is another solution that fits in with the wording, though may not be in the spirit of the problem.

I like the optical illusion, but does it actually have anything to do with the problem?

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Wouldn't just an entire big square work? 3x4, still uses 12 matches. Plus, the problem didn't say all the rabits couldn't be together.

post-2327-1193258557_thumbjpg

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wouldn't this also work (provided my drawing skills... or lack thereof, are excused)?

The matches usually tend to be always the same size. The ones in your picture aren't. The ones that are diagonal are longer than the other ones.

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I had assumed that the requirement was that the floor area of each new area should be the same as previouslly. It's a long time since I studied geometry but I think the solution given does this whereas most (if not all) of the alternatives offered do not!

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The solution of author is wrong.

He wrote the same area?

the cell area on the first picture is P=1/2a*a where a is lenght of match for ex=10

so area of 1 cell will be 50

on his picture we have equila teraltriangle so P=(a*a*square root(3))/4 where a is lenght of match for ex=10

so are of 1 cell will be 43,30

on my solution

right-angled triangle so P=a*a/2 where a is lenght of match for ex=10

so area of 1 cell will be 50

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The solution of author is wrong.

He wrote the same area?

the cell area on the first picture is P=1/2a*a where a is lenght of match for ex=10

so area of 1 cell will be 50

on his picture we have equila teraltriangle so P=(a*a*square root(3))/4 where a is lenght of match for ex=10

so are of 1 cell will be 43,30

on my solution

right-angled triangle so P=a*a/2 where a is lenght of match for ex=10

so area of 1 cell will be 50

so you claim that my solution:

1. does not offer the same (equally big) area for 6 rabbits

2. made of 12 matchsticks

???

post-2-1197756565_thumbgif

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Yes If it is in 2d your solutions is wrong.

Maybe rabbits will have enough space ;-) but it will be less than on the begining.

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