Given P=(a/b+c/d)*(e/f+g/h) ,
where a,b,c.., ...h are 8 distinct positive integers, all below 25 and all fractions are proper fractions, find the highest and the lowest values of P.

Rem: P&P solution preferred.

For largest, we want both parentheses to be large and the fractions to be as close to 1 as possible:
(24/25+18/19)*(22/23+20/21)=3.640980713

For smallest, we want one parenthesis to be as small as possible and all fractions as small as possible:
(2/25+1/24)*(4/23+3/22)=.0377503294

I only tried a few things, so a more exhaustive search may find an idea I missed.

The 25 limit seems artificial.  If my solutions are optimal, they can probably be generalized.

**Edited to replace a missing digit and fix another minor typo.

Edited on September 23, 2014, 9:19 am

Posted by Jer on 2014-09-22 09:15:13