Hello, metlx!

There are at least 2 necklaces.

On each necklace there is the same number of diamonds, on each at least 2.

If we knew the number of all diamonds, we would also know the number of necklaces.

The number of all diamonds is bigger than 200 and smaller than 300.

How many necklaces is there?

. .

There is no formula for this problem.

It is an exercise in reasoning and logic.

Let = number of necklaces.

Let = number of diamonds on each necklace.

So there is a total of: . diamonds . . . and:

And we are told: if we know , we'd know the number of necklaces.

. . [A powerful clue!]

Suppose has twodifferentprime factors.

. . For example: .

Then we could havetwoscenarios:

. . 7 necklaces with 29 diamonds on each.

. . 29 necklaces with 7 diamonds on each.

The only way we'd besureof the number of necklaces

. . is if the two factors areequal.

The only square of a prime number in that range is: .

Therefore, there are 17 necklaces with 17 diamonds on each . . . answer (B).