Jonathan Thomson's web journal

How Big is Lily Pad Lake? November 4, 2012

Filed under: Uncategorized — jethomson @ 8:53 pm

Here’s a common brain teaser:

“In a lake, there is a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?”

 

Many people answer a bit too quickly and say 28 days. However, the correct answer is 47 days assuming the doubling on the 48th day doesn’t overshoot the area of the lake. On the 47th day the lily pads cover half of the lake and on the 48th day they double covering the entire lake. But what I’m really interested in is how big is Lily Pad Lake?

 

Let’s denote the area of lily pad Lake by A.

 

Then the area covered by the lily pads on the 48th day is A. Therefore the formula for determining the area covered by the lily pads on day n is:

 

On the 48th day Alily is equal to A, and on the 0th day Alily = A/(2^48). The problem doesn’t state how many lily pads are present on the 0th day, but to minimize the size of Lily Pad Lake I’ll assume just one lily pad is present. Thus on the 0th day Alily is equal to the area of 1 lily pad. Assuming the area covered by one lily pad is 5 square feet, then:

 

That’s 1.4 quadrillion square feet or 50,482,628 square miles or 130,749,410 square kilometers. For comparison purposes the Pacific Ocean is 155,557,000 square kilometers and the next biggest ocean is the Atlantic at 76,762,000 square kilometers. So perhaps a better name for Lily Pad Lake would be Lily Pad Ocean, which would have to be a freshwater ocean since lily pads don’t live in salt water.

 

 

Notes
Typical [lily pad] plant size 5-10′ square

The Pacific Ocean is 155,557,000 sq km

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