My instructor from college gave our class a puzzle to solve today.
He asked us how many triangles there are in the picture below. The answer I got was 32 and said there were more. How many can you find? He said there were something between 40 and 50. I think he's bull $hi!!ing us.

i can get 32...my coworker got 36

Wow, that was fast. Impressive.

yea but how do you get 40-50?? that's what i'm aiming for

I seriously doubted finding anything over 32 and I'm amazed your co-worker got 36. lol I think my instructor is trying to play games with our minds.

33 and a headache! I guess you need to print out 20 or so and get a colored pencil to really get it right. That way you could check every possibility.

yeah i got to 24 then I was not sure if i was counting the same triangles again or not... OK I started over again, 30 before I started getting unsure again.

that's what i did...i grabbed some colored markers and began dotting the points of each triangle...i could only get 32 total

my coworker did it all in his head so perhaps he counted some of them more than 1 time...he stands by the fact that he got 36 "so far", however

ok, made me print it out... fine. 32 bah, yeah either we are all missing something really obvious or more than 32 is B.S.

Originally posted by Lufa
ok, made me print it out... fine. 32 bah, yeah either we are all missing something really obvious or more than 32 is B.S.

Yea, I nearly pulled the hair off my head trying to find just 1 more but started to have a really bad headache so I gave up :p

Whoo i see 34... gonna have to do some ms paint and post it... keep looking.

That is not to bad, for the air force officer test they give you an a shape and you have to find that shape inside of a bunch of other random lines and in some of them it looks like it has more than one shape in it. Oh yea, you get 15 mins to find 30 of them. That was the hardest part of the test.

I'm getting 35.....

10 single triangles,
10 2-piece triangles,
5 3-piece triangles on the outside,
5 3-piece triangles on the inside (using the pentagon in the middle)
5 5-piece triangles (from one corner to the opposite side edge)


Seems to make sense that the solution would be divisible by 5, since it's basic shape is pentagon-symmetric.....?

So if you find one solution, there SHOULD be 4 more just like it....

Ok here is what I got... 35 quick break down
10 light blue, individual triangles
3 greens on top
6 reds on the sides
6 dark blues on the bottom
8 purples in the middle
2 browns that took me forever too see

Plus a bunch more triangles in case someone sees some more.

People in class thought I was hardcore when I was putting a letter next to each corner of the puzzle and naming them out on piece of paper. You two (threeputtwash and Lufa) on the other hand brings a new meaning to the word lol Good work Lufa for finding two more.

I found 42 so far, I remember doing this before, and it is possible to get at least 50.

Originally posted by BRx8
i can get 32...my coworker got 36

tell your friend, he double counted.

http://www.coolmath4kids.com/triangle2sol2.html

yes I know the solution I offer is more of a pentagram than a box with a triangle on top, but I assure you the solution is still the same. it makes it easier to visualize the way it is on the kids website.

I'm thinking he is right. I counted 35 when I did it, and counted the exact 35 he counted using the same strategy (count the single triangles, then the ones using 2 pieces, 3 pieces, then 5 pieces) so if you find one he didn't, let me know.

I got 48 :confused:

pmacwill... look again at the image that is posted in this thread... it's not exactly a Pentagon shape... it's more of a house looking thing. Thus it's possible to have multiple differences in the shape.

Originally posted by Outlaws eXtreme
pmacwill... look again at the image that is posted in this thread... it's not exactly a Pentagon shape... it's more of a house looking thing. Thus it's possible to have multiple differences in the shape.

Nope.....in this case, the shape does not make any more lines or straighten any (combining) lines. So whether the left or right sides are parallel, or the whole thing is symmetric will yield the same results.

Those that claim more than 35, please show us where the triangles are (compared to Lufa's diagrams)....

Really... show us the goods please.

Counting a totally different way I got 35 as well.

-Mr. Wigggles

Originally posted by threeputtwash
Nope.....in this case, the shape does not make any more lines or straighten any (combining) lines. So whether the left or right sides are parallel, or the whole thing is symmetric will yield the same results.

Those that claim more than 35, please show us where the triangles are (compared to Lufa's diagrams)....

The shape is a different triangle. On your example, of course in a Pentagon shape enclosure, you'll have similar shaped triangles. But in this diagram, they are different in proportion.

In Lufa's examples, he's missing about 5 right off the bat. If I have more time after dinner, I'll copy and paste what I have for now. It's about 47-48 now. I'm losing 2 somewhere.

Originally posted by Outlaws eXtreme
The shape is a different triangle. On your example, of course in a Pentagon shape enclosure, you'll have similar shaped triangles. But in this diagram, they are different in proportion.

In Lufa's examples, he's missing about 5 right off the bat. If I have more time after dinner, I'll copy and paste what I have for now. It's about 47-48 now. I'm losing 2 somewhere.

That's perfectly fine. The triangles are in a different shape, but just because the picture is askew, does not change the NUMBER of triangles.

Say you have a square with two diagnol lines through it. Now you take two opposite corners and stretch the square (into a rhombus). You did NOT create any triangles, and you did NOT remove any triangles, by shifting the lines.

Unless you add an actual line to the polygon, or manipulate the lines to intersect into a totally different way (in this case, it's only manipulated in a similar way), you have the exact same amount of triangles (just shaped differently).

Again, we might have over looked a few triangles, but then it means that the same triangles were overlooked in an equilateral pentagon too.


Again, feel free to show us the triangles that we have missed....
:)

Originally posted by Outlaws eXtreme
If I have more time after dinner, I'll copy and paste what I have for now. It's about 47-48 now. I'm losing 2 somewhere.

Is dinner over yet? Snarf that Dominoes and be done with it already! :D

ive got 38 so far. i have some colorized pics i will try to post

It is only mathematically possible to extract 35 triangles, given the current configuration.

There should be 44.

You guys either need to check your math or your geometry because you either missed out on probability and statistics in High School and don't remember how to get the proper permutations and combinations of 11 or you forgot that a triangle only has 3 sides and three vertices.
The correct number is 35.

So does the RX8 have 237hp or not?

Originally posted by hotpot
So does the RX8 have 237hp or not?

Mine does, yours does not.:p

dinner is taking forever...

Yeah gotta love message boards.

I found 500 triangles but I am simply too busy to back up my claim :).

Look at it as a three dimensional image. More will come out.

Look at it as a three dimensional image. More will come out.

More than 35 will emerge?

I got 36. Each color is a triangle. Some can be doubled due to symmetry; the counts are noted next to the shape.

Heres the pic

I JUST RECOUNTED MY COLORIZED PICS. IT SEEMS I DOUBLE COUNTED THE 2 IN PRODS LAST COLORED IMAGE. I REVISE MY COUNT TO 36.

PLEASE SHOW THE MATH THAT GIVES 35 AS AN ANSWER. I DIDN'T TAKE PROBABILITY AND STATISTICS IN MY HIGH SCHOOL MATH CLASS IN 1986 AND DID NOT GO TO COLLEGE SO I AM UNAWARE OF THE EQUATION TO BE USED HERE.

Nope.....35. You counted one twice...

BAH! Good call... 35 it is.

crap i also counted that one twice- i again revise my count. i agree with 35. really i would like to see the math on this.

Maybe it is easier to visualize if the original puzzle is drawn with an equilibrious (linearly symetrical) pentagon.
There are seven groups of triangles shown in the diagrams below. Each group consists of exactly five triangles with every triangle rotated 72° around the center of the pentagon; one triangle from every group is highlighted in the respective diagram. So the total number of the triangles in the pentagon is 7x5=35.
There are 7 combinations with 5 permutations each.
There are no other combinations of the shapes contained in the pentagon that produce triangles.

Originally posted by MazdaManiac
Maybe it is easier to visualize if the original puzzle is drawn with an equilibrious (linearly symetrical) pentagon.


Elegant, simple and definitive. Nice job.

wait... so was the instructor high on chalk when he was claiming 40 & change?

Thanks guys, all this was very interesting. What exactly have we learnt here? :)

Uh, those that can - do. Those that can't - teach?

Okay...how many triangles in this one?

too many...

-JiM

I don't seem to care anymore after Guy's thread about the universe.

Originally posted by GiN
wait... so was the instructor high on chalk when he was claiming 40 & change?

Well many schools and colleges use whiteboards nowadays, but I believe he was possibly high off the marker he was using to draw the picture on the board! So far, many have come to the conclusion that there are 35 triangles. However, there are still a few on this board that claims there are 50... I would like to see that with pictures. Otherwise we are sticking with 35 :p .

Originally posted by hotpot
Thanks guys, all this was very interesting. What exactly have we learnt here? :)

some of us can't color/count very well:o

ABC ABD ABE ABF ABI ABJ ACD ACE ADE AEG AEI AEJ
AFJ AGI AIJ BCF BCI BDJ BEH BEI BEJ BFI BHI BIJ
CEI DEG DEJ EGJ EHJ EIJ FHI FIJ GHJ GIJ HIJ

Total: 35

Verticies are:

A
B C D E
F G
H
I J

ABC ABD ABE ABF ABH ABM ACD ACE ACF ADE ADF ADH
ADJ AEF AFJ AFM AGH AGI AGJ AGK AHI AHJ AHK AHL
AHM AHN AIJ AIK AJK AJL AJM AJN ALM ALN AMN BCH
BDH BFM BGH BHL BLM CDH DDH DDJ DEJ DFJ DFM DHI
DHJ DHM DIJ DJM EFJ FJK FJN FMN GHL GJL HIM HJL
HJM HJN HKN HLM HLN HMN IJM JKN JLM JLN JMN

Total: 71

Originally posted by markh711
ABC ABD ABE ABF ABH ABM ACD ACE ACF ADE ADF ADH
ADJ AEF AFJ AFM AGH AGI AGJ AGK AHI AHJ AHK AHL
AHM AHN AIJ AIK AJK AJL AJM AJN ALM ALN AMN BCH
BDH BFM BGH BHL BLM CDH DDH DDJ DEJ DFJ DFM DHI
DHJ DHM DIJ DJM EFJ FJK FJN FMN GHL GJL HIM HJL
HJM HJN HKN HLM HLN HMN IJM JKN JLM JLN JMN

Total: 71

My God, you are a machine.:eek:

My God, you are a machine.

No, I just told the machine how to do it. :)