Saturday, December 27, 2008

Ponder this!!

An Idle mind is devil's workshop.. I have been jobless this week. Killing time big time.. Just then thought I can get back to my habit of solving puzzles and found this.. Try it out..

A monkey (hypothetical one) is trying to scale a slippery pole (Does this sounds familiar?) that is 10,000 feet high (obviously hypothetical!!). While trying to climb up the pole, the monkey starts with the second number in the Fibonacci series (1) and goes up by one foot. The pole being very slippery he slips and slides down by a distance equal to the previous number in the series which in this case is again 1. Thus after the first attempt he is back to where he started, 0. He tries harder in each subsequent attempt and manages to go up by the next number in the series, but unfortunately again slides back by the distance of the previous number in the series. Thus in his second attempt he manages to go up by 2 feet and then slides down by 1, a net gain of 1 feet. Like wise in the third attempt it goes up by 3 feet and slides down by 2 and so on.

For every 3 attempts he slips by an additional cumulative distance of 10 feet. Obviously the monkey is getting tired! Thus after the 3rd attempt the monkey slips by an additional 10 feet, after the 6th slips by an additional 20 feet, after the 9th slips by an additional 30 feet and so on. Also, he cannot slip back any further than the ground level (0 feet). (We don’t expect the monkey to slip underground.)

Finally here is the question. How many attempts would the monkey take to reach the top of the pole,if at all??

Update:: One attempt consists of climbing up and slipping down..and there is nothing like an half attempt ;-)

4 comments:

Goutham said...

20 attempts?

Srikanth said...

No maga.. 20 is not the right answer..

Goutham said...
This comment has been removed by the author.
Goutham said...

Ok. I considered the monkey reaching the top of the pole in the middle of an attempt which you say is not an option. Now the answer is clear :)