I am wondering whether the following set-up of the DJ-algorithm makes sense:

Alice collected all  bills (banknotes) of a certain series, i.e., all bills marked XYZ (series) + numbers, from 00…000 to 11…111 (in binary basis), so altogether she has collected 2^n bills. She knows that in any series (i) either all banknotes are fine or (ii) exactly half of them are counterfeited.

Bob has a quantum checking device: when the series* is introduced on its pad for any binary string x_1x_2x_3…x_n (number on the bill) it calculates f(x_1x_2x_3…x_n), a function which takes two values – 0 [“the bill is fine”] or 1 [“the bill is false (counterfeited)”]. Now Alice wants to know what did she get.

*communicated to Bob by Alice through a standard classical channel