So that probability is greater than 0.999,
and the reason for that is the only way she wouldn't be caught
is if the two people she spends the bill with
take exactly the same challenge.
The challenge is 10 bits long,
so the probability that would happen
is 1/2^10--1 in 1,024.
And 1 minus that is greater than 0.999.
So that's pretty high.  If that's not good enough, we could increase m.
