# How many triangles do you see?

Asked by Dutchess_III (40148) 5 days ago
Observing members: 0 Composing members: 0

18?

ragingloli (45037)

7

JLeslie (57481)

All of them.

canidmajor (15011)

5

nerdgirl578 (1060)

12

anniereborn (11531)

Every time there is a new answer I look at the picture again. Lol.

JLeslie (57481)

Now I see nine…

nerdgirl578 (1060)

I’m seeing 18.

Demosthenes (7049)

I see 18 too now, I wonder if there’s more?

nerdgirl578 (1060)

You people in the high numbers are counting trapezoids and other shapes. I don’t know if my number is right, but I’m pretty sure numbers like 18 must be wrong.

Or, I could be wrong. Lol. I might be missing some.

JLeslie (57481)

@JLeslie You’re wrong. :) There are at least 18, but it took me a while to see it

nerdgirl578 (1060)

No, they aren’t @JLeslie.

Dutchess_III (40148)

I see my mistake. Now, I’m at 12.

Edit 16

Lol. Oy.

JLeslie (57481)

Raggie is correct. :D

Dutchess_III (40148)

You mean ragingloli? 18?

JLeslie (57481)

Yes. I have called him Raggie since Wisdm days.
Yes. 18

Dutchess_III (40148)

Other people had 18 too. That’s why I was confused.

That was fun! Thanks.

JLeslie (57481)

I didn’t get it right off the bat either, even though I knew exactly what to do because I do this stuff a lot. I’d never done this one before though.

Dutchess_III (40148)

I liked how very simply they broke it down!

Dutchess_III (40148)

I see 36 without my glasses on.

flutherother (29657)

Him?

rebbel (28876)

Her?

Dutchess_III (40148)

At first I was counting the trapezoids, and then I thought I had caught my mistake—caught the trick, but then I obviously had missed a bunch of the triangles in the end.

JLeslie (57481)

Her

rebbel (28876)

Ok.

Dutchess_III (40148)

18. If we label the columns c1, c2 and c3, we can combine columns as: c1, c2, c3, (c1 and c2), (c2 and c3) and (c1, c2 and c3). That is 6 ways of combining columns. The triangle can include 1, 2 or 3 rows. 3×6=18.

The number of ways of selecting the columns is 3 + 2 +1. Here is why. If the leftmost column is c1 then the rightmost column is c1, c2 or c3. If the leftmost column is c2 then the rightmost column is c2 or c3. If the leftmost column is c3 then the rightmost column is also c3. Adding up the possibilities, we get 3+2+1. If there were n columns, the number of ways of combining them would be n + (n-1) + n-2) + ... +1 = n(n+1)/2, using the formula for arithmetic series.

There are 18 triangles in the picture and one in the question.

Pinguidchance (3637)

4

stanleybmanly (19991)

I don’t want to explain & blow it for the late arrivals.

stanleybmanly (19991)

Damn That’s tricky. I’m up to 6

stanleybmanly (19991)

Yep. It’s gotta be 6. There are 3 at the apex and the horizontal lines form the bases of the remaining 3. Who found others?

stanleybmanly (19991)

You are the late arrival @stanleybmanly! ♥ Here Ya go. :D

Dutchess_III (40148)