The average number of marbles in 3 bottles is 52. The difference between the number of marbles in the biggest bottle and the number of fishes in the smallest bottle is 31. No two bottles have the same number of marbles. Find the largest possible number of marbles in the biggest bottle.

Answer 1

not sure what to do about the fishes, but we know there are 3*52 = 156 marbles in all. So let's say that the marble amounts, from smallest to largest, could be
52 52 52 - nope, not all different
51 52 53 - works for me.
...
52-15 52 52+15 = 37 52 67 - also works, but maybe you're looking for
37 51 68 where the largest has 31 more than the smallest