math problem

[skates]

TomCowley is correct. The non-bracket weigh-off for second is more efficient and the answer is 21. Can someone give me a purely mathematical explanation of WHY the non-bracket weigh-off becomes more efficient? I can demonstrate it to myself, but I'm asking for the conditions that make it so, and how we can intuitively see this as being optimal.

The difference in this case is that using a non-bracket weigh-off leaves a worst case scenario of 4 contenders for 3rd place as opposed to the 5 contenders given by a bracket weigh-off.