I have in mind 4 positive numbers, which I would like you to find.

Out of the set of 6 pair-wise products of those numbers I am going to omit one.

The remaining five are: **8,10,12,24,30. **

(In reply to

re(3): Solution with Analysis by Ady TZIDON)

All three irrational sets you listed are permutations of each other. To see this express all the values in the form sqrt(a/b) for a,b coprime.

My original irrational set (the one Steve listed) becomes {sqrt(20/3), sqrt(48/5), sqrt(15), sqrt(60)}. Your two additional sets are {sqrt(15), sqrt(60), sqrt(20/3), sqrt(48/5)} and {sqrt(48/5), sqrt(20/3), sqrt(60), sqrt(15)} which are just permutations.