The Missing Dollar
The logic in this calculation is flawed. The net money paid by the three men plus that kept by the bellboy should not necessarily equal the total money in the system, $30 in this case. Defining
- S = Initial payment (total money in the system) ($30)
- B = money kept by the bellboy ($2)
- N = net money paid by the three men ($27)
- P = the money held by the three customers ($3)
- T = N + B, the calculation being tested against S ($29)
The following relations are obvious:
T = N + B
N = S - P
Combining the above equations yields
T = S + B - P
This shows that T and S are not equal unless the money returned to the customers equals that held by the bellboy, which is not the situation in this problem.