So, for 10 pairs, 45 guesses (9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1) in the worst case, and roughly half that on average?

It's interesting how close 22.5 is to the 21.8 bits of entropy for 10!, and that has me wondering how often you would win if you followed this strategy with 18 truth booths followed by one match up (to maintain the same total number of queries).

Simulation suggests about 24% chance of winning with that strategy, with 100k samples. (I simplified each run to "shuffle [0..n), find index of 0".)