Kind of an interesting problem. Complete sorting in a timely manner is basically not possible because of the physical reality of 100k pieces of paper. But maybe you can group the bills into 100 piles of "last 2 digits", so then for each lookup you "only" have to check 1000 bills. And then later, while searching a group, you can take the time to further sort them by the 3rd digit. I guess it also depends on how long you expect the contest to go on, i.e. how many lookups you will do.
Even with the simplified grouping strategy, let's be generous and assume it takes you 3 seconds to look at a bill, figure out what to do with it, and physically move it to the correct place. That's still 83 person-hours to do a single pass and put the bills into 100 groups for quicker lookup. With 2 people, that's 5 full 8 hour days of non-stop sorting.