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09-05-2018
08:22 AM

09-05-2018
08:22 AM

Puzzle only to fun. Question graphs are made by using Mathcad programing.

Divide a surface into two equal sized areas by using matchsticks.

1. With using two matchsticks.

2. With using three matchsticks.

3. With using n>3 matchsticks.

Solved! Go to Solution.

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Accepted Solutions

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11-30-2020
10:20 AM

11-30-2020
10:20 AM

22 REPLIES 22

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09-05-2018
09:35 AM

09-05-2018
09:35 AM

Re: Divide a surface into equal sized areas

That's a no-brainer. I have very large match-sticks, so I can divide the triangle into two pieces of equal size with a single match-stick, using a variety of positions of the stick.

And if it can be done with one, it can be done with any number of match-sticks.

But I think that's not what you're after, and you implicitly assume some rules that you have not explained.

Luc

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09-05-2018
10:43 AM

09-05-2018
10:43 AM

Re: Divide a surface into equal sized areas

Assuming that only match-sticks with length 1 may be used, and they must be only inside the triangle, here is a solution for 2 match-sticks.

Luc

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09-05-2018
04:59 PM

09-05-2018
04:59 PM

Re: Divide a surface into equal sized areas

Here's a second solution using two match sticks:

An additional puzzle: Using four matchsticks divide the triangle area in three areas of equal size.

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09-06-2018
02:27 AM

09-06-2018
02:27 AM

Re: Divide a surface into equal sized areas

Good answers!

Both of you using Mathcad and it will be help for Machcad usage for the users.

Match stick puzzle usually use unit length 1 and it put on dot points on the figure of the stick top or bottom.

Or the position can be fixed by using match sticks.

If you got two and three stick answers, you can arrange them any number of this problem.

Then, using 12 all sticks in my picture and move two or more sticks to reduce the area size from 4*3/2=6 to 5, 4,3 and 2. I don't know the answer the area size is 1. Of course the minimum movement number of the sticks are the good answers.

Tokoro.

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11-29-2020
06:39 AM

11-29-2020
06:39 AM

Re: Divide a surface into equal sized areas

The one of 3D.

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11-29-2020
03:25 PM

11-29-2020
03:25 PM

Re: Divide a surface into equal sized areas

Ttokoro, It seems something like this :

Best Regards.

Loi.

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11-29-2020
03:30 PM

11-29-2020
03:30 PM

Re: Divide a surface into equal sized areas

And It seems to be as half-volume, too. ?

Regards.

Loi.

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11-30-2020
07:41 AM

11-30-2020
07:41 AM

Re: Divide a surface into equal sized areas

1/4th.

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11-30-2020
10:20 AM

11-30-2020
10:20 AM

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12-01-2020
04:03 PM

12-01-2020
04:03 PM

Re: Divide a surface into equal sized areas

One more third divide by a plane would output a 1/8 V.

Regards.

Loi.

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12-01-2020
08:57 PM

12-01-2020
08:57 PM

Re: Divide a surface into equal sized areas

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12-02-2020
03:31 AM

12-02-2020
03:31 AM

Re: Divide a surface into equal sized areas

Thanks for your hint, Tokoro. And it seems this is half-volume of "frame".

Regards.

Loi.

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12-03-2020
06:52 AM

12-03-2020
06:52 AM

Re: Divide a surface into equal sized areas

Nice Job! Oden for kudos.

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12-04-2020
08:10 PM

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12-05-2020
02:48 AM

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12-05-2020
04:30 AM

12-05-2020
04:30 AM

Re: Divide a surface into equal sized areas

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12-06-2020
01:19 PM

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12-07-2020
10:33 PM

12-07-2020
10:33 PM

Re: Divide a surface into equal sized areas

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12-08-2020
03:03 AM

12-08-2020
03:03 AM

Re: Divide a surface into equal sized areas

It seems this is last surface patch that I have known about that rotation. (And It seems to divide a surface of regular dodecahedron into equal sized area.)

Best Regards.

Loi.

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12-08-2020
02:52 PM

12-08-2020
02:52 PM

Re: Divide a surface into equal sized areas

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12-09-2020
10:35 PM

12-09-2020
10:35 PM

Re: Divide a surface into equal sized areas

Rotation and divide a surface into equal sized areas. (divide by 6 sticks)

Regards.

Loi.

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01-05-2021
12:51 PM

01-05-2021
12:51 PM

Re: Divide a surface into equal sized areas

Tokoro, there are two more other planes that divide a surface into equal sized areas :

Best Regards.

Loi.