Sister's Math Problem

[J_V]

My sister is trying to pass this basic math course with this really annoying teacher and the only way she is going to do it is if she gets the extra credit. The only hitch is you have to get all the problems totally correct or you get no credit. This is the only one that is simple for me. If you guys could help, it would make my day /images/graemlins/smile.gif. It's not really a math problem.

http://www.photodump.com/direct/jvspree/triangle.jpg


How many triangles are in this diagram?

And yes, it really is my "sister's" /images/graemlins/smile.gif.

Is there a mathematical way to solve this?

[jason_t]

I used cleverness and math and got (7 + 6 + 5 + 4 + 3 + 2 + 1) * 3 = (7 * 8 * 3) / 2 = 84.

This is what they're teaching math courses? Sigh.

[ChromePony]

sounds about right to me

each of the 3 'rows' can be the base of a trianlge, with a width of 1,2,3,4,5,6 or 7 segments. There are 7 possible that are 1 wide, 6 that are 2 wide... 1 that is 7 wide.

3 rows -> 3*(7+6+5+4+3+2+1) = 84

[superleeds]

[ QUOTE ]
(7 * 8 * 3) / 2

[/ QUOTE ]

Why this bit? Genuinely curious

[jason_t]

[ QUOTE ]
[ QUOTE ]
(7 * 8 * 3) / 2

[/ QUOTE ]

Why this bit? Genuinely curious

[/ QUOTE ]

Because 1 + 2 + ... + n = [n * (n+1)] / 2.

Reason:

s = 1 + 2 + ... + n
s = n + (n-1) + ... + 1

add column by column.

2s = (n+1) + ... + (n+1) = n * (n+1)

so that

s = n * (n+1)/2

[ihardlyknowher]

How many trapezoids?

OOT got this wrong. Let's see if SMP can do any better.

[jason_t]

[ QUOTE ]
How many trapezoids?

OOT got this wrong. Let's see if SMP can do any better.

[/ QUOTE ]

Also 84.

[ihardlyknowher]

[ QUOTE ]
[ QUOTE ]
How many trapezoids?

OOT got this wrong. Let's see if SMP can do any better.

[/ QUOTE ]

Also 84.

[/ QUOTE ]

Righto.

[superleeds]

neat. thx.

[Patrick del Poker Grande]

[ QUOTE ]
How many trapezoids?

OOT got this wrong. Let's see if SMP can do any better.

[/ QUOTE ]
OOT got it right. Justin A and then jason_t got it wrong, then ChromePony agreed, but it was fixed (before The Trainwreck got it right).

[sirio11]

From point "A" there are 8 "diagonals".

To form a triangle you need to use 2 "diagonals"

The number of ways to choose 2 diagonals from a set of 8 is

8C2 = (8*7)/(1*2) = 28

Now, every pair of diagonals can form only 3 triangles (there are 3 "rows")

So, total number of triangles is 28*3 = 84

[ChromePony]

[ QUOTE ]
OOT got it right. Justin A and then jason_t got it wrong, then ChromePony agreed, but it was fixed (before The Trainwreck got it right).


[/ QUOTE ]

Yeah yeah i screwed it up in OOT, but I can never think properly in that atmosphere.

[Timer]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
(7 * 8 * 3) / 2

[/ QUOTE ]

Why this bit? Genuinely curious

[/ QUOTE ]

Because 1 + 2 + ... + n = [n * (n+1)] / 2.



[/ QUOTE ]

Correct me if I'm wrong, but wasn't it Euler who came up with this solution [1 + 2 + ... + n = [n * (n+1)] / 2] when he was a child at school? Or at least he independently discovered the solution as a child . . . or do I have him mixed up with someone else?

[sirio11]

It was F. Gauss

[jason_t]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
(7 * 8 * 3) / 2

[/ QUOTE ]

Why this bit? Genuinely curious

[/ QUOTE ]

Because 1 + 2 + ... + n = [n * (n+1)] / 2.



[/ QUOTE ]

Correct me if I'm wrong, but wasn't it Euler who came up with this solution [1 + 2 + ... + n = [n * (n+1)] / 2] when he was a child at school? Or at least he independently discovered the solution as a child . . . or do I have him mixed up with someone else?

[/ QUOTE ]

Gauss.