Monkey problem: find order for 1/2, 1/4, 3/4, 3/5, 5/6,11/15

[mallet]

My friend sent me this interesting little teaser and I can't solve it at all! Can anybody help me? Thanks.

A little monkey had 75 peaches. These are the fractions he used to decide what to keep over the next few days.

1/2 , 1/4 , 3/4 , 3/5 , 5/6 , 11/15

In which order did he use them so that he ended up with just one peach left at the end?

Mallet.

[stapel_eliz]

I think this was the nRich contest question back in December of 2004. You can check their site for the archived solution.