# Superman 3

## The Movie

Superman 3 is a 1983 2nd sequel to the original Superman movie, starring Christopher Reeve. The movie is infamous for one of the “get rich” schemes in the movie, where a worker exploits rounding in the weekly paycheck to make himself rich. This same plot point is reused in the later 1999 film Office Space, more successfully this time. It’s often known as a “salami slicing” scheme.

You can view the trailer for the movie below:

## Math Scenario 1: Trimming Fractions of a Cent

The character Gus gets a paycheck for $143.80. One of his co-workers points out that in reality his pay was probably a fraction of a cent more than that, but it was rounded down.

Gus is inspired to write a program that collects all these extra fractional half cents, but is busted after giving the game away driving his new Ferrari.

Most similar schemes in history have involved not taking fractions of a cent, but rather simply small amounts of money that might not be noticed, in the range of a few cents per account.

Let’s say you work for a large multi-national corporation, and have access to their salary payment system. If there are 400000 employees, and the average fractional cent amount you can trim from each week’s pay is 0.3 cents, work out the annual earnings you would get.

*Earnings = amount per person * number of people * number of weeks per year*

*Earnings = 0.3 cents * 400000 * 52*

*Earnings = 6240000 cents*

*Earnings = $62400*

This amount, while very nice, is still less than the average annual salary in Australia as of 2016.

There are other more lucrative schemes you can try however…

## Math Scenario 2: Overcharging Customers

Another version of this tactic is to slightly overcharge or skim the accounts of customers for services or products in the hope that they don’t notice, or to charge accounts small amounts and then not offer refund options.

This approach is slightly more detectable in that the difference is no longer hidden in a “rounding error” – if the customer knows what they should be getting charged and is paying attention, they will detect this technique.

Let’s say a criminal is planning to skim $10 per account, but each time they do so they run a 0.1% chance of getting caught.

How much money can they steal without their risk of getting caught going above 50%?

*Risk of getting caught = 1 – chance of being safe*

*Risk of getting caught = 1 – (chance of success per account)^#accounts*

We can re-arrange this based on what we know:

*(chance of success per account)^#accounts = 1 – risk of getting caught*

*(chance of success per account)^#accounts = 1 – 0.5*

*(chance of success per account)^#accounts = 0.5*

Then take the log of both sides:

*(chance of success per account)^#accounts = 0.5*

*log[(chance of success per account)^#accounts] = log(0.5)*

#accounts * *log(chance of success per account) = log(0.5)*

#accounts* = log(0.5) / log(chance of success per account)*

#accounts* = 692.8*

At $10 per account, that leads to:

*Total amount = #accounts * amount per account*

*Total amount = 692.8 * 10*

*Total amount = $6928*

## Real-Life Example: Fuel Station Scam

A real-life variant of this scam had a group of men install computer chips in fuel pumps that said that more fuel had been pumped into cars then had actually been done [1].

Let’s say you’re the unscrupulous owner of a fuel station, and you rig your pumps to say that the fuel pump has pumped 10% more fuel into a customer’s car than it has in reality. So if the gauge reads 40 litres, the car has only actually received 36.36 litres of fuel.

Let’s say you bought fuel whole sale for $1.30 per litre and sold it at an average of $1.32 per litre.

If you normally sold 200000 litres of fuel per week, we can calculate how much extra money the scam will net you per week.

First we can calculate earnings without the scam:

*Profit = income from fuel – cost of fuel*

*Profit = 200000 * 1.32 – 200000 * 1.30*

*Profit = $4000*

With the scam going, you will still sell what appears to be 200000 litres of fuel to customers, but will only have to buy 10/11th of that amount in actual fuel:

*Profit = income from fuel – cost of fuel*

*Profit = 200000 * 1.32 – 200000 * 1.30 * 10/11*

*Profit = $27636.36*

The net difference is:

*Net earnings from scam = earnings with scam – earnings without scam*

*Net earnings from scam = 27636.36 – 4000*

*Net earnings from scam = $23636.36*