I'm fairly certain that's correct, unless you can point out where you think I made a mistake.
Read carefully-that says inclusive!
Count how many integers are in that range, which is 20-10+1=11. Now divide that by the total number of choices, which is 99-0+1=100. So, your answer would be 11/100, if I'm not mistaken.
The triangle part has got me stumped, but then, I haven't really given it a lot of thought.
Find the prime factorization of 715 first, and you will realize that there is only one answer that will work.
Also, this problem has the audacity to assume we know common English words! Outrageous. Just kidding. I don't know why I said that.
If you solved it yourself, good for you!
Actually, could you tell me how you got your answer? I'm curious.
Notice that each unique case can be expressed as a line. For example, if the y-coordinate is three times the x-coordinate, then we can say that y=3x. Do you see how this can help?
It does? Well, I've never had that happen to me, but that's interesting.
Nevermind. I see that you said writing problems.
I think what you said seems obvious, though I suppose if you paraphrase it they have no way of knowing.
Notice that 2400 is just 24*100. So, it will have the prime factors of 24 times plus those of 100, which are 2^2+5^2. Added together, that makes 8 primes.
You raise a good point although many people will just ignore it. It's an honor code, and AoPS has no way of enforcing it.
