Can 5 be written as a product of fractions in this set?

W = {2/1, 5/3, 8/5, 11/7, 14/9 ...} = {(3n + 2)/(2n + 1) : n ≥ 0}

Repetitions are allowed.

Note: Extra credit: Same question for 10 and 20.

None of the numbers containing an even number in the numerator can be used, as there would be no factor of two in any of the denominators, and therefore any integers produced would be even.

That includes 2/1--it can't be used, so the largest number from the set that can be used is the 5/3. Any number you use is at most 5/3. Even 5/3, when cubed, is less than 5, so you need at least four fractions from the set. But each fraction is more than 3/2, and (3/2)^4 is over five.

So no set can be chosen to produce a product of 5.

Posted by Charlie on 2013-08-28 15:50:03