hardmath

You want to hire a temporary employee for one month. You offer him reasonable wages, but the employee suggests an alternative. For the first day of work, he will be paid a penny. For the second day, two pennies. For the third day, four pennies. The salary for each subsequent day will be double the previous day's, until the one month term is over. Ignoring the legalities of such a situation, would it be a good idea to accept the potential employee's proposal?

Not at all. He'll earn $5,368,709.12 on the thirtieth day alone.

Why this works

This riddle plays with the concept of exponential growth. On the first day, the employee earns one penny, and each subsequent day, his pay doubles—meaning on day two he earns two pennies, day three he earns four, and so on. By the thirtieth day, his pay skyrockets to over five million dollars because the doubling effect compounds rapidly. The trick lies in understanding how quickly exponential growth accelerates, which can often be surprising and leads to the conclusion that this seemingly small offer turns into a huge financial burden.

Common Wrong Answers

“It sounds like a good deal because he starts with a low amount.”

While the first day's pay is low, the exponential growth means the overall salary will become astronomically high, far exceeding any reasonable wage for a temporary position.

“He will only earn a few dollars by the end of the month.”

This guess miscalculates the exponential nature of the doubling pay. By the end of the month, the total will be in the millions, not just a few dollars.

“He will earn the same amount every day, which is manageable.”

The salary structure is not constant; it doubles every day. This leads to a rapidly increasing total that becomes unmanageable very quickly.

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