Guess I’l do it
First things first, a graph where all dots (representing the triangles) are connected to two and two only of the other elements is necessarily made of separate loops (convince yourself of this)
Now, in any single loop of triangles, look at them on the table: there are traingles with one side facing up and others with one side facing down. The only way a triangle can connect to a side-up to share a side is to be side-down, and vice versa. So it’s necessary for every loop to have an even number of triangles, since if it was odd, at one point we’d necessarily have 2 connected triangles that are oriented in the same way (and that’s impossible ;D)
Now for another one!
3b) A, B and C are playing with 2008 skittles. ‘A’ brings down three times the skittles brought down by ‘B’, and ‘B’ him/herself brings down double the number of C’s skittles. (They are all playing the same match, so the skittles they have brought down as a total can’t exeed 2008)
What is the maximum number of skittles A could bring down?
And come on guys, 1) is not that hard, there is a nice formula to calculate the number of divisors, look “divisor” up on Wikipeida