So here's how I solved it: 50 creatures - 6 sharks = 44 creatures in the 3 sections Section 3 can have 1, 3, 5, 6, or 7 sharks in it. 44 - 1 = 43 43 is prime, so, that's not right 44 - 3 = 41 41 is prime 44 - 5 = 39 39 is not prime What's the first number that's divisible into 39 (excluding 1) 3 39 / 3 = 13 All the variables fit the requirements.

5 sharks (in Gamma) 3 fish per tank 13 tanks (7 tanks in Gamma)

Set up a spreadsheet and go the same result. Actually, there are two (2) valid results that equal 50 total organisms, except it results in the same number of sharks in Gamma, so can be discounted.

The really clever bit was using thermal imaging to find fish in water .. how did they do that? Thermal imaging doesn't work through water, never mind seeing cold blooded animals that are the same temperature as their surroundings.

Oh man, this solution was SO MUCH MORE ELEGANT than mine!!!

I worked out how many sharks there would be for every single permutation of 1, 2, 3, 4, 5, 6, 7, 8 fish, and so on, and then crossed out all of the answers where the number of sharks in gamma was the same number of sharks in either of alpha or beta.

man I did this completely different I worked with "they say no more than 13 so let's assume there are 13 total" then 6f+6s=12t+7fg=19t 31 is too many sharks 12f+6s=28t+14fg=42t 8 is too many sharks 18f+6s=24t+21fg=45 5 sharks fit guess I got lucky

50 creatures - 6 sharks = 44 creatures in the 3 sections

Section 3 can have 1, 3, 5, 6, or 7 sharks in it.

44 - 1 = 43

43 is prime, so, that's not right

44 - 3 = 41

41 is prime

44 - 5 = 39

39 is not prime

What's the first number that's divisible into 39 (excluding 1)

3

39 / 3 = 13

All the variables fit the requirements.

5 sharks (in Gamma)

3 fish per tank

13 tanks (7 tanks in Gamma)

Math.. noooope. Shit goes extinct every day, fuck 'em this will make for healthier sharks.

I worked out how many sharks there would be for every single permutation of 1, 2, 3, 4, 5, 6, 7, 8 fish, and so on, and then crossed out all of the answers where the number of sharks in gamma was the same number of sharks in either of alpha or beta.

Man, I did so much extra work...

I worked with "they say no more than 13 so let's assume there are 13 total"

then 6f+6s=12t+7fg=19t 31 is too many sharks

12f+6s=28t+14fg=42t 8 is too many sharks

18f+6s=24t+21fg=45 5 sharks fit

guess I got lucky

T= Tanks in sector Gamma

S= Sharks in sector Gamma

(4f+2)+(2f+4)+(Tf+S) = 50

(6+T)f = 44-S

S = 1,3,5,6,7

T = 0,1,2,3,4,5,6,7

f = 1,2,3,4,5,6,7

(1 Shark ) (6+T)f = 43

(3 Sharks) (6+T)f = 41

(5 Sharks) (6+T)f = 39

(6 Sharks) (6+T)f = 38

(7 Sharks) (6+T)f = 37

f =/= 1

f =/= 2

f = 3 works for 39 (5 Sharks)

f =/= 4

f =/= 5

f =/= 6

f =/= 7

(6+7)3= 44-5

7 Tanks in sector Gamma

5 Sharks in sector Gamma

3 fish in each tank

2+4+5 = 11 sharks, 2+4+7 = 13 tanks, 13 x 3 = 39. 39+11 = 50.