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The Tripling Algae (illustration)
FILE No.103Unsolved

The Tripling Algae

Difficulty ★☆☆about 5 minLogic PuzzleExponentsWorking backward
Algae that triples every day covers a pond on day 20. On what day was one third of the pond covered?

Case Record

Algae is growing in a pond. Every day it triples its area. On day 20, the whole pond was covered.

Your question

On what day was one third of the pond covered?

Case Files

Diagram

Algae coverage of the pond (triples daily)DayShare of the pond covered18?19?20Whole pond (100%)Each day the area is 3 times the day before.
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

What fraction was it the day before?

Open hint 2

Think of the opposite of tripling.

Open hint 3

What happens when one third of a pond triples?

Solve It

Your question

On what day was one third of the pond covered?

Choose the answer closest to the truth.

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The Truth

Day 19

The answer is "Day 19."

Because the area triples each day, the day before the pond is fully covered it was one third covered. If the whole pond is covered on day 20, then day 19 is the day with one third.

On day 7 or day 10, tripling each day would never reach the full pond on day 20. Day 18 is one ninth.

Work backward from day 20DayShare coveredChange20Whole×3191/3×3181/9×3171/27If the whole pond is covered on day 20, one third was covered on day19.
Diagram of the solution

Key Points

  • Trace the growth backward
  • "One third" is one day before the full pond
  • Do not confuse proportional and exponential growth

Why people get fooled

Because you divide instead: "one third of 20 is about day 7."

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