Problem Solver 8 #6?

Question

Problem Solver 8 #6?
As a marine bioloigist on the submarine Neptune, Petra is charting the number of fish in specific areas of the oceans. She is currently survying an area in the front of the sub. The rooms are arranged on 3 sides. One day a Petra was counting the fish, she saw 20 fish threw the windows of rooms A,B,C, and D; 20 fish in the windows of rooms D,E,F and G; and 20 fish in the windows of rooms G,H,I and J. She saw a different number of fish in each room. How many fish did Petra see through the window of each room?

Someone please answer this!!!

Answer 1

It's clear all numbers are between 1 and 14. If 1 was not one of the numbers, then the numbers would have to be between 2 and 11. Since we need 10 different numbers that would take them all. So the total would be 65 which is too much. Actually the sum of the 10 numbers has to be less than 60, so it's 55 =1+...+10. These are the numbers. Clearly D+G= 60-55=5. So you could have (1,7.10.2)(2,9,6,3)(3,4.5.8). This is just one solution. there are others but not many.