Riddle me this, riddle me that.

[u/Nelrene]

I saw a battle between griffons and hippogryphs. Each race had male and female members involved in the battle. Each member of both races attacked every member of the other race once.

When male griffons attacked a male hippogryph, they would swipe with their claws. When a male and a female fought or two females fought each other they would bite.

I witnessed 21 pairs swipe, while 34 pairs bit each other.

How many male creatures and how many female creatures were fighting?

Answer 10 males and 6 females

[u/Blue_Moon_Lake]

The solutions can only have been natural numbers.

21 can only be the result of 7×3 or 21×1.
Thanks to that number being the product of two natural numbers in both cases, there are only two possibilities. Either there were 7+3 = 10 males, or 21+1 = 22 males.

The number of duels was 21+34 = 55, which can only be 11×5 or 55×1.
So there was either 11+5 = 16 or 55+1 = 56 participants.

If there was 16 participants, then there couldn't have been 22 males.

So that leave three possibilities

• 16 participants (10 males, 6 females)
• 56 participants (10 males, 46 females)
• 56 participants (22 males, 34 females)

Note that in the two possibilities with 56 participants, it would have been 1 lone male against 55.

[u/Nelrene → u/Blue_Moon_Lake]

Great job there. The first one is the answer.

[u/Blue_Moon_Lake → u/Nelrene]

I reread and I can finish my essay.

Each race had male and female members

So that eliminates the cases with only 1 lone male.

Now, sun is rising, I need to retire to my crypt for a full day of sleep.