The “Infinite Profit” Puzzle

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Let’s say I put $20 in a box. Now you do the same. The box now contains $40, and we’re both aware of this fact. Now, I sell you the box for $30. We both walk away with $10 profit.

Repeat forever, and you’ve got an infinite supply of money. Wait, wut?

At first glance, this brain teaser might raise eyebrows, but once you recognize the fallacy and work it out, your dreams of early retirement come to an abrupt end…

This is an example of the “hidden-cost” fallacy, which occurs when you ignore relevant costs into your calculations. A common hidden-cost fallacy is to ignore the opportunity cost of capital when making an investment or shutdown decisions.

On to the puzzle’s solution…

You put in $20 in the box (-20), you then sold the box for $30 (+30).

-20 + 30 = +10

So you have a profit of $10.

Your friend put in $20 in the box (-20), then gives you another $30 for purchasing the box (-30), and then gets $40 from the contents of box (+40) because they bought it off you.

– 20 – 30 + 40 = -50 + 40 = $-10

Your friend has lost $10.

In other words, your friend had a revenue of $40, but a cost of $50, making this far from infinite money for both you and your friend.


This puzzle is similar to the fast talking in the Abbott and Costello skit, “Two Tens for a Five“…