Question

Each of six islands is populated by storks. The whole colony consists of 20 storks. One evening, all of the storks ate 35 frogs in total; moreover, any 2 storks from the same island ate the same number of frogs, while any 2 storks from different islands ate different numbers of frogs. No stork was left hungry. How many storks ate 2 frogs?

Answer 1

I have no idea how to put this in an algebraic form for you. But if I can give you what I found, maybe that can help you along.

There's 6 islands, 20 storks, 35 frogs.
Every stork ate at least 1 frog. And every island has at least one stork.
The amount of frogs eaten by a stork depends on the island they're at and needs to be different for every island.

On island A, we have at least 1 stork that ate 1 frog each (=1 frog)
On island B, we have at least 1 stork that ate 2 frogs each (=2 frogs)
On Island C, we have at least 1 stork that ate 3 frogs each (=3 frogs)
On island D, we have at least 1 stork that ate 4 frogs each (=4 frogs)
On island E, we have at least 1 stork that ate 5 frogs each (=5 frogs)
On island F, we have at least 1 stork that ate 6 frogs each (=6 frogs)

So 6 storks were already divided over 6 island, that leaves 14 storks
21 frogs were already eaten, that leaves 14 frogs.

We also know that every stork eats at least 1 frog, so 14 storks / 14 frogs, is one frog per stork.

So every island only has 1 stork, except island A that has 15 storks in total that only eat 1 stork.

The answer is that only one stork ate 2 frogs