Math puzzles

[jxu]

Start off easy.

#1
Find the number of ordered triples (a, b, c) where a, b, and c are positive integers, a is a factor of b, a is a factor of c, and a + b + c = 100

[AFtExploision]

(5, 20, 75)

[tyler569]

200.

102 if you don't count 1 as a factor.
I wrote some code to calculate this for arbitrary sums which I will post when I am not on my phone.

Fun fact: if b must also be a factor of c, that number drops to 20.

http://pastie.org/9495201
(Briefly) tested working on python2.7 and 3.4

[jxu]

You are not allowed to use a calculator or program a solution.


#2 (more easy)
Solve for a17 when a1 + a2 + a3 = 1, a2 + a3 + a4 = 2, ... a16 + a17 + a1 = 16, a17 + a1 + a2 = 17

[Iceglade]

Here's a really easy (but still interesting) one:

Is 362887 prime or composite? Don't try to factor it, look for a trick (and try to generalize!)

[jxu]

I dunno, it was faster to do trial division

[Iceglade]

I dunno, it was faster to do trial division

Well that's damn boring.

hint: what is 362880

[jxu]

Oh it's 9!
I don't know if you expected anyone to know that off the top of their head