For a positive integer n > 2, consider the n-1 fractions 2/1; 3/2; ...; n/(n-1).

The product of these fractions equals n, but if you reciprocate (i.e. turn upside down) some of the fractions, the product will change.

How can you make the product equal 1?
Find all values of n for which this is possible.

(In reply to Different solution by Jer)

My error was in thinking the sequence would end on a prime.  I don't know why it was not occurring to me that primes in consecutive fractions can cancel out just fine :

4/5 * 5/6 the fives cancel.  No need to go to 10. 

Posted by Jer on 2015-12-02 14:05:17