Math Brain Teaser (1 Viewer)

[Rollie]

A certain water lily grew extremely quickly and doubled its surface area each day. At the end of the 30th day, it had entirely covered the pond in which it lived. If a second water lily identical to the first had been planted in the pond, how long would the two lilies have taken to cover the entire pond?
A friend of mine e-mailed this to me knowing I'd be ripping my hair out trying to solve it!
The only answer I could come up with was Spoiler:15 days but that seems a bit obvious. Any thoughts?
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[Edited last by Rollie on November 14, 2001 at 07:14 PM]

 

[Carlo_M]

I don't think so:
Spoiler:If it doubles its CURRENT surface area every day, then on the 29th day it would have been 1/2 the size of the pond, thus doubling on the 30th day to cover the entire pool. So wouldn't it take 29 days for both lilies to cover the pond?
[Edited last by Carlo Medina on November 14, 2001 at 07:18 PM]

 

[Patrick_S]

Perhaps someone can correct me but there really isn’t enough information provided to precisely say how long it would take two lilies to cover the pond.
After all, at the end of the 29th day it could have covered ¾ of the pond and then doubled to cover the entire pond on the 30th day. Since we don’t know the precise figures involved a precise day is impossible to nail down.
[Edited last by Patrick_S on November 14, 2001 at 08:02 PM]

 

[BrianW]

Assuming it just covers the pond on the 30th day, then two lillies would require Spoiler:29 days to cover the pond.
Bonus question: It was later discovered that the lilly pad sucks up water as it grows, so that the pond's surface area shrinks by one-fourth every day. Knowing this, how long does it take for the single lilly pad to cover the shrinking pond, given that it will cover the pond in thirty days without the pond shrinking?

 

[Clinton McClure]

Is it an African or European lily?

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[MichaelPe]

I don't see why this is difficult...
2^30 = 2*(2^29)
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[Bill Catherall]

Bonus question: It was later discovered that the lilly pad sucks up water as it grows, so that the pond's surface area shrinks by one-fourth every day. Knowing this, how long does it take for the single lilly pad to cover the shrinking pond, given that it will cover the pond in thirty days without the pond shrinking?

I got Spoiler:approximately 21.12 days.
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Bill

 

[Chauncey]

I got:
Spoiler:Solve for:
2^X = 2^30 * (3/4)^X
X = LN(2^30)/((LN(2)-LN(3/4)) = 21.20 Days
And who thought you didn't need logarithms.

Someone let me know if I am incorrect.
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[BrianW]

Man, you guys are good!

 

[Jeff Blair]

Now this is starting to get a little scary.

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[McPaul]

Who ever thought we'd actually need all that math stuff we learned in school??
ok... well.... not actually NEED...
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[Ron-P]

I got Spoiler:A Headache
Peace Out~

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[Brett_B]

Ron-P,

 

[Joseph Howard]

Ooh! Can I play?
Teaser Number II:
Gino and Maria were strolling in the countryside one day when they came to a lake. They noticed a pole stuck in the middle of the lake. They rowed out to where the pole was in the lake to get a better look. After getting an up-close look they returned to shore. They found a local resident and asked him about the pole. They were told that one-half of the pole was lodged in the ground, another one-third of it was covered by water, and 11 feet of the pole is sticking out of the water. What is the total length of the pole in feet?
Dr. Joe

 

[Mike Broadman]

66

 

[Carlo_M]

I concur with Mike. And with Ron-P.

 

[Trey Fletcher]

To solve these problems, simply give it the old college try: Spoiler:Get a case of beer and a pizza and worry about it tomorrow.

 

[Richard Cooper]

I got:
Spoiler:Beaten to the headache joke by Ron-P

[Edited last by Richard Cooper on November 15, 2001 at 02:29 PM]

 

[Bill Catherall]

Try this one out:
What's the missing number?

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Bill

Edited to fix image.

 

[Sania M]

259?