# Snail climbing a tree stump

A snail is slowly climbing a tree stump. The stump height is 100 cm.

At day, the snail manages to climb 20 cm upwards.

At night, while sleeping, the snail slips 10 cm downwards.

After how many days will the snail reach the top of the tree stump?

• 4 day if he sleep upside down – Kepotx May 23 '18 at 10:58
• This is such a classic puzzle, I thought this must be a duplicate, but I can't find earlier mentions. It is usually framed as a snail in a well, not on a tree stump. – Jaap Scherphuis May 23 '18 at 11:30
• There is an earlier one -- puzzling.stackexchange.com/questions/248/… -- but it was deleted for being a simple mathematics problem rather than a puzzle. (FWIW, I think it is a puzzle, albeit one both very easy and very well known.) – Gareth McCaughan May 23 '18 at 11:41
• @Kepotx : I remembered this from school, loong time ago. I could not find it, and thought it would fit here :) – KYL3R May 23 '18 at 12:53
• A sentiment expressed in a comment on the now-deleted question @Gareth mentioned points out that while there is a twist to this question that makes it something beyond a mere math problem, "that twist is so trivial I'm not sure you can really call this a good puzzle". I'm personally inclined to agree; there's not enough puzzle here for me. – Rubio May 24 '18 at 10:09

The snail will reach the top after

9 days.

This is because

the snail essentially climbs 10 cm per day. After 8 days (and nights), it is at a height of 80 cm. The day after, it climbs the remaining 20 cm to the top and doesn't slip down anymore.

Another way to see why this is the solution1, is to

1. see that the snail climbs to a height of 20 cm in the first day.

2. After the first night (slipping down 10 cm) and second day (climbing 20 cm), it has climbed 10 cm to reach a height of 30 cm.

3. Every following night + day will help the snail climb 10 cm further: after the third day, it has reached a height of 40 cm, after the fourth day it reached 50 cm, et cetera.

4. Thus, after the ninth day it reaches 100 cm, the height of the tree stump.

________
1 Thanks to Jaap Scherphuis for suggesting this way of explaining the solution.

• Your solution looks at it as (day+night)+(day+night)+(day+night)+...+(day+night)+day. I find the explanation a bit cleaner if you look at it as day+(night+day)+(night+day)+..., so that you are always looking at the peaks of where the snail gets to. It completely takes the 'twist' out of the solution. – Jaap Scherphuis May 23 '18 at 12:32
• Thank you @Jaap! I have edited that way of explaining the solution into my answer. – Just a student May 23 '18 at 13:23

9 Days

Explanation:

Day 1:- Ascent:20 Descent:10 Total:10
Day 2:- Ascent:20 Descent:10 Total:20
Day 3:- Ascent:20 Descent:10 Total:30
Day 4:- Ascent:20 Descent:10 Total:40
Day 5:- Ascent:20 Descent:10 Total:50
Day 6:- Ascent:20 Descent:10 Total:60
Day 7:- Ascent:20 Descent:10 Total:70
Day 8:- Ascent:20 Descent:10 Total:80
Day 9:- Ascent:20 Descent:NOT REQUIRED Total:100

• Hello and welcome to Puzzling.SE! Good answer (even if it was already discover). Usually, answer are embed in spoiler tags, using ">!" so you can't see the answer by mistake – Kepotx May 23 '18 at 13:16
• Also correct, make a graph! :P – KYL3R May 23 '18 at 13:36