A patch of algae in a backyard pool doubles in size every day.
On day 30, the algae covers the whole pool.
On which day did it cover exactly half of the pool?
On day 30, the algae covers the whole pool.
On which day did it cover exactly half of the pool?
💡 Hint
Doubling works both ways: one day before, it was half as big.
Reveal answer
On day 29.
Because the algae doubles every day, the amount on day 30 is twice the amount on day 29. If day 30 is the whole pool, day 29 must be half the pool. Answering “day 15” treats the growth as steady, adding the same amount every day, when in fact it doubles. With doubling, most of the growth happens at the very end.
Did you know?This puzzle is a classic way to explain exponential growth. On day 25, the algae covers only about 3% of the pool (1/32), so the owner might not even notice it. Five days later, the pool is completely green. The same pattern shows up in compound interest, viral videos and population growth: things look small for a long time, then suddenly they are everywhere.
Did you get it?
About This Puzzle
Summer vacation, an unattended backyard pool, and a patch of algae that grows faster than anyone expected. This puzzle is about how doubling really works.
How to Think About It
The tempting move is to cut 30 in half. Instead, think backward. If something doubles every day, what did it look like one day before it filled the pool completely?
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