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What is the answer...
...to this brainteaser?
A frog sits on a lily pad in the precise middle of a circular pond with a
radius of 6m (19 feet).
He jumps straight towards the edge of the pond a distance of 3m (9 ft 6 ins)
but this tires him and so every subsequent jump is precisely half the
distance of the jump before (i.e. 1.5m (4ft 9in), 75cm (2ft 4in), etc). How
many jumps does it take him to get to the edge of the pond?
x
A frog sits on a lily pad in the precise middle of a circular pond with a
radius of 6m (19 feet).
He jumps straight towards the edge of the pond a distance of 3m (9 ft 6 ins)
but this tires him and so every subsequent jump is precisely half the
distance of the jump before (i.e. 1.5m (4ft 9in), 75cm (2ft 4in), etc). How
many jumps does it take him to get to the edge of the pond?
x
Scroll to see replies
Reply 1
Technically he never gets there- every jump halves the distance, but the frog will end up jumping an infinitesimally small distance... then half that... then a microscopic distance... then half that... technically he can't get to the edge.
FadeToBlackout
Technically he never gets there- every jump halves the distance, but the frog will end up jumping an infinitesimally small distance... then half that... then a microscopic distance... then half that... technically he can't get to the edge.
Not if he makes it to the edge before he ends up doing that. I don't know if he does, but still.
EDIT: It would appear he doesn't make it. Never mind.
Juwel
Good old Zeno and his ugly paradoxes again.
Well, the reason I posted was because it was in a Mensa book, and we've put the question on something, and then subsequently lost the book.
So everyone here was working on the Xeno's paradox theory, in that each time the frog halves the distance between itself and the destination. You can't divide the distance by 2 and reach it, instead you'd just get very very close.
However, it has been found in the last few minutes, and it just says the answer is 41.
Reply 9
He never gets there, cos he lands in the water, and you can't jump on water.
Reply 11
The answer is never. However, there may be a point where the numbers get so small that you allowed to round up or get frisky with error margins
Taken literaly, it is impossible for him to ever reach the bank.
Taken literaly, it is impossible for him to ever reach the bank.
Reply 13
Notebooksecrets
He never gets there, cos he lands in the water, and you can't jump on water.
I agree. Enough of all this smelly maths and equasions. Frog lands in water. The End.
King Leigh
Well after 41 jumps, he'd still have a whole 1.354e-12 metres to go. If you wish to count that as at the bank, so be it, but why would he not be there with only 2.728e-12 metres left (40 jumps)??
Stupid book.
Stupid book.
Lol, I agree! Despite it being a Mensa book.
We printed this brainteaser in a newsletter and now I have no idea what answer I should write. All the book says is 'the answer is 41.'
Not very helpful, an idea of how they get to that/equation etc would be nice!
Reply 15
Ignore the book's answer. It is wrong, if the question is to be taken literaly.
Just post "never" as your answer, and explain why.
Just post "never" as your answer, and explain why.
Reply 16
Huzzah! I can do maffs, me! 
Reply 18
The answer is 41 actually.
He has to cover a distance of 6m in total. He initially covers 3m and then covers 1/2x + 1/4x + 1/8x+1/16x..
If you calculate it till the 41st degree you'll find you get 6m.
He has to cover a distance of 6m in total. He initially covers 3m and then covers 1/2x + 1/4x + 1/8x+1/16x..
If you calculate it till the 41st degree you'll find you get 6m.
Are you sure?
If the first jump covers half of the distance, and every jump after that halves, surely the sum of all the following jumps can't be more than first (so never making the remaining 3m)?
Like binary numbers... each number is half of the last, and the sum of all the preceding number make exactly one less than it. So 8 > 4 + 2 + 1 or 512 > 256 + 128 + 64 + 32 ...
In the same vein, surely 6 > 6/2 + 6/4 + 6/8 ... ?
If the first jump covers half of the distance, and every jump after that halves, surely the sum of all the following jumps can't be more than first (so never making the remaining 3m)?
Like binary numbers... each number is half of the last, and the sum of all the preceding number make exactly one less than it. So 8 > 4 + 2 + 1 or 512 > 256 + 128 + 64 + 32 ...
In the same vein, surely 6 > 6/2 + 6/4 + 6/8 ... ?
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