Lily Pad Riddle: How Long to Cover Half the Pond?
Reasoning test on a quantity that doubles at each step
The riddle
A lily pad doubles its surface area each day. It takes 48 days to completely cover a pond. After how many days does the lily pad cover half the pond?
Need a hint?
Work backward from the day the pond is fully covered, and ask what the surface was the day before.
Show the answer and the solution
Answer: 47 days: the day before the pond is fully covered, since the surface doubles each day.
The reasoning
If the surface doubles each day, the surface on day 48 is twice the surface on day 47. On day 47, the lily pad therefore covers exactly half the pond, since doubling half gives the whole. Intuition pushes toward 24 days, half of 48, but this is a mistake, because the growth is not linear. The lily pad therefore covers half the pond after 47 days, that is, the day before it fully covers the pond.
What next?
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