Which three numbers multiplied together equal 1000?

Answer 1

There are infinitely many possible triplets.

Suppose A is any positive real number that is less than 10 = cuberoot(1000).

Let B be any positive real number between A and sqrt(1000/A).

And let C = 1000/(A*B).

This construction ensures that in each triplet (A, B, C), A < B < C so that each triplet is different and the same set is not being counted multiple times.

Then, A*B*C = A*B*1000/(A*B) = 1000

There are infintely many real numbers smaller than 10, there are therefore infinitely many choices for A.

Then there are infinitely many real numbers between A and sqrt(1000/A), so there are infinitely many choices for B.

Consequently, there are infinitely many possible solutions.

Answer 2

10 x 10 x 10