Difficulty: Fun
An adventurous snail decides to climb up a wall to the roof of a school. The snail can climb up 3 metres in a day but slides back down 2 metres at night! If the school is 12 metres tall, how many days will it take the snail to reach the roof?
Need a hint?
It’s not 12 days! It might be tempting to think the snail simply goes up 1 metre per day because it slides down at night… once it reaches the roof, it won’t slide back down!
Brainteaser answer
The snail gets to the roof in 10 days.
With all the climbing and sliding, it might be tempting to summarise the snail’s progress as one metre per day. And that’s helpful to a point but it doesn’t capture the situation when the snail reaches the roof during the day. See, the snail won’t slide back down if it reaches the roof!
So, when does the snail get within striking distance of the roof? That would be at 9 metres because once the snail gets to 9 metres, it can climb the last 3 metres in one day. That’s the last day of its climb.
Now we can ask, how many days will it take to get to 9 metres? That would be 9 because we know the snail will keep climbing up 3 and sliding down 2 for a total of 1 metre per day and night combined.
All up, that’s 9 days of climbing and sliding plus the last day’s climb to the roof. 10 in total!
There’s also another way to think of the question that might make it simpler.
On the first day, the snail reaches a high point of 3 metres up the wall. The next day, it starts with a 1 metre head start, so it’ll make it to 4 metres up. Continue this pattern, increasing the head start by 1 metre per day, and you’ll find the snail will reach 12 metres on day 10!
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