## Frog stuck in a well

In the bottom of a well, 45 feet deep, there was a frog that started traveling toward the top. In his journey, he ascended 3 feet every day, but fell back 2 feet every night.

In how many days did he get out?

*[submitted answers will show in about a day]*

Couple months back, a similar math brain teaser was posted.

Alexey| Guest July 11th, 2007 - 5:02 am43

Mark W| Guest July 11th, 2007 - 5:10 amOn the 43rd day the frog ascends from 42 ft. to 50 ft. so it is on the 43rd day that the frog reaches the top.

Mark W| Guest July 11th, 2007 - 5:11 amaaah! I mean the frog ascends from 42 ft. to 45 ft. on the 43rd day!

Justin| Guest July 11th, 2007 - 5:54 amI guess that as he makes net progress of 1 foot per day the answer would be 1 day per foot until he got within 3 feet of the top and then one day more fot the last 3 feet as he would be able to leave the well before slipping down the following night.

With that in mind I make it 43 days in total.

charity| Guest July 11th, 2007 - 6:11 am43 days

jason| Guest July 11th, 2007 - 6:56 am43 days

Daniel| Guest July 11th, 2007 - 8:26 am43 days

Joe| Guest July 11th, 2007 - 8:53 am43 days?

Shawn| Guest July 11th, 2007 - 9:26 am43 days

On the 43rd day the frog jumped up 3 feet from his previous night’s height of 42 feet, and escaped the well.

He might have escaped sooner, but Lassie only helps humans. Actually, collies are known for their particular disdain for amphibians at large.

Sala| Guest July 11th, 2007 - 10:19 amThe frog should ascend for 21 days to exit the 45-feet well.

Scott K| Guest July 11th, 2007 - 11:07 amits gotta be something like 42. he climbs up 1 foot every day total but when he gets to 42 the 3 he climbs in the day will get him out and he wont need to climb anymore or fall back. 43 ill say, 42 to get to 42 and then 1 more day.

ED| Guest July 11th, 2007 - 2:32 pm42 days

Jay| Guest July 11th, 2007 - 3:21 pmI guess it depends… 43 days if the frog makes it to the edge of the well and climbs out or 44 days for it to pass the mark…

Rasool| Guest July 11th, 2007 - 4:41 pm43 days

Robert L| Guest July 11th, 2007 - 9:05 pm43 days to reach the top, but you know honestly unless frogs are a lot tougher than me I don’t think he ever made it. I mean he would have starved by then lol.

John Lewis Highsmith| Guest July 11th, 2007 - 11:09 pm43, unless he is stupid, and then it will be 44

andi| Guest July 11th, 2007 - 11:22 pmAfter 42 days, he’s up 42 feet. On the 43rd day, he ascends the 3 feet to the top.

biobot| Guest July 12th, 2007 - 2:55 am41 days because on the 41st day he would clear the last two feet without slipping back down. (ie. he’d jump out of the well)

keith| Guest July 12th, 2007 - 7:11 am43

azri| Guest July 12th, 2007 - 9:38 am43

Mike| Guest July 12th, 2007 - 11:41 am45 days… one foot each 24 hours

milo zachary| Guest July 12th, 2007 - 12:45 pm43 days. Every day he gained one foot, so he began each day at the level of the preceeding day’s number, so on day 42, he began at 41 feet, and climbed to 44 feet. On day 43, he began at 42 feet and climbed to 45 feet and was out.

Ian mckinnon| Guest July 12th, 2007 - 2:46 pm42

Amie Krone| Guest July 12th, 2007 - 3:43 pmI’m going to guess – 44 days.

Megan W| Guest July 12th, 2007 - 4:27 pmFirst of all, yes, I did have a lot of time on my hands…

The graph illustrates progress made each day (in green) and lost each night (in red).

I conclude that the frog takes 44 days to exit the well, because though the frog reaches 45 feet on day 43, this just means that he is at the top of the well… not beyond it.

44 days.

Megan W| Guest July 12th, 2007 - 4:52 pmThe image didn’t show in my previous comment, so the link is here if anyone could be bothered accessing it!

http://a174.ac-images.myspacec.....2807d5.jpg

RK| Profile July 12th, 2007 - 5:33 pmHi Megan- don’t think the graph made it?

I believe the point you raise is similar to what Jay is saying, and is probably why Joe put a ‘?’ after his answer of 43 (and might explain John Highsmith’s comment and Amie’s answer of 44)

Not sure what others think – while the ‘official’ answer is ’43’, in light of the way the question is worded- aren’t ’43’ & 44′ both acceptable?

Ituri| Guest July 13th, 2007 - 5:42 amThe frog will ascend 1 foot each day for 42 days and on the last day it’ll ascend 3 feet (because no night spent in the well on this day). Thus, the frog will exit the well on the 43rd day since beginning its climbing.

Scott K| Guest July 13th, 2007 - 7:28 pmwhat kind of rock is the well made out of, thats the real question.

Angelo| Guest July 14th, 2007 - 6:19 amIt took the frog 45 days to get out of the well. You subtract 3 feet from the original height (froggy going up) then add 2 after subtracting the original height from 3 (froggy going down).

RK| Profile July 19th, 2007 - 9:47 amI suspect Shamrock

Nir| Guest July 24th, 2007 - 11:20 pmYou are all wrong except for Amie and Megan.

The correct answer is 44. I have programmed a flash simulator of this which you can try out yourselves, available on my website with the source code included.

http://www.motion2.net/frog.html

Enjoy

Nir| Guest July 24th, 2007 - 11:34 pmOooops, my bad. I made a programming error, the correct answer is 43. Amie and Megan are wrong.

See my simulation

http://www.motion2.net/frog.html

Hendy| Profile June 23rd, 2011 - 12:41 pmOn the 43 day. The frog would be able to jump high enough to get out and would not need to fall back that night.

nadia| Profile September 20th, 2011 - 8:33 am43