A medium question on climbing out of a well for P3, with a step-by-step solution, diagrams and the answer. Rarely set directly in competition papers, but a classic for learning to think about the last step on its own. Good for the younger years.
The question
A well is 21 m deep.
A frog at the bottom jumps up 5 m each day and slides back 1 m each night.
As soon as it reaches the top during a day, it is out and does not slide back.
On which day does the frog get out?
Show the hints (2)
💡Hint 1: After the last jump there is no slide. How high must the frog be at the start of its last day?
💡Hint 2: Before that, how much does a whole day (up by day, down by night) gain? How many whole days to reach that height?
Worked solution
Have a go first, then read the solution step by step.
1.The last day's jump is 5 m, so before it the frog needs to be at 21 − 5 = 16 m or higher.
2.At 4 m a day: 16 ÷ 4 = 4 exactly, so it takes 4 whole days (4 × 4 = 16 m).
3.On day 5 it jumps 5 m and is out.
⚠️Common mistake: 21 ÷ 4, answering day 6 — the last day has no slide.
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