making a "hat trick" sort of game

[idontknow]

i'm thinking of making a game house in my quest that features a "hat trick" game--basically, after a sequence where an item is shown inside one of 3 identical boxes where the boxes switch positions multiple times, link must find the box w/ the item inside--i know how to make the house, including the entrance screen where link pays to play & all that, but i'm not sure how to make the sequence where the boxes move. I figure i'll have to use cloral's multi-warping trick, but i've mastered that already--it's just a matter of figuring out how to use tiles & combo-cycling to make the sequence where the boxes trade places. Anyone have any ideas? (to get a better idea, this is like the "hat trick" game at like the the white sox games where a ball is under a cap & they quickly trade places & you have to carefully keep your eye on the cap & at the end, you have to guess which one has the ball)