Question

Another one.
A dice is rolled thrice. The numbers appearing are noted and if possible, Constructed a triangle with.
Find the ratio of the number of Scalene tringles possible to isosceles triangles that could be made.

Answer 1

I have calculated quite roughly. But is it something like 22/107? This could be very stupid, but the hazards are all mine.

Answer 2

Ummmmm. No.
Numerator is either 5 or 7. Not sure.
Not 22.

Answer 3

Given answer for Numerator is 5. (Not sure about accuracy)
Still, basic condition you applied?

Answer 4

there are 6 choose 3 or 20 combinations for possible scalene triangles
only 6 will work
2,3,4
2,4,5
2,5,6
3,4,5
3,4,6
4,5,6

for isosceles triangles, there are 30 possibilities
21 will work, 9 will not
-these will not
anything with two 1's
2,2,4
2,2,5
2,2,6
3,3,6

--> ratio = 6/21 = 2/7

Answer 5

So the denominator may be correct? I posted for ratio isosceles to scalene.

I have another answer that is 7 to 22 (scalene to isosceles)

Answer 6

@dumbcow 5,3,6 too, right?

And Did you employ trial and Error or something else?

Answer 7

Apporv.
7 seems correct.
I'm getting 21 for isosceles.

Answer 8

See the isosceles possibilities according to me are:

221
223
332
332
334
335
441
442
443
443
445
446

and same way 5 possibilities each for the 55.. and 66.. series)

so that is. '21" (i had miscalculated it as 22 earlier)


Now for scalene triplets, i list the ones which are not possible:

123
124
125
126
134
135
136
145
146
156
235
236


that is about 12

now no. of ways of choosing 3 nos. out of 6 is 6C3. that is 20. minus the no. of possibilities. so 20-12 = 8

so, scalene to isosceles =8/21

Answer 9

Know that's a very crude method, and I may have missed out a couple, according to dumbcow's answer.

Answer 10

Also 6C3 Doesnt apply here.
You have a total 6*6*6 = 216 possibilities.

Answer 11

oh yeah another that is not possible in the scalene part "246"

so it becomes (20-13)/21
=7/21

Answer 12

Ohhhhhh wait.

Answer 13

You reduced it without that in the first step.
Yes that works 6 C3

Answer 14

6C3 yes. am applying them for "scalene triplets". that is abc where a b and c none are the same.

Answer 15

Thanksguys.
So 7/21 it is.
Though it took time right?
And You just have too use a+b>c by trial and error?
Thats just too long.
Something shorter to cut the time short?

Answer 16

Hmm, yes if you are a master of PnC. (Though it didn't take much time as I counted pretty systematically, but accuracy is always an issue then.)

Answer 17

Exactly. I tred Integral solutions usng a dummy varible. Didnt help too much.

Answer 18

oh sorry guys, yeah i missed one ---> 7/21 it is
and yes i just counted which combinations would work one-by-one
30 possible isosceles
20 possible scalene