Puzzler of the week

[Scott MacLean]

This week's puzzler:

Okay, let me set the scene. A guy is building a new house. As luck would have it, his entire back yard is dirt.

He's planning on having a big Fourth of July celebration. So he goes to the local nursery, and he says to the clerk, "I've got to buy some grass seed, because it's almost June 1, and I'm having a party on July 4th. I want a yard full of grass!"

The fellow at the nursery says, "We have this new product. It just came in a few months ago; you may be interested in it. It's a plug of grass. It's about the size of your fist. You plant this in your lawn in a central location, and every day it doubles in size. You only need one."

The customer says, "You mean, if I plant this thing on June 1, by June 30 I'll have a lawn?"

And the guy says, "Well, according to my calculations, no problem. Then, you spray the lawn with an arrester spray, so it doesn't subsume your car."

The customer then asks, "You're sure you did the math correctly?"

To which the clerk responds, "I'm telling you -- plant one of these and in 30 days, you'll have a full lawn in your backyard."

The customer thinks about it, and then says, "Great, but just to be on the safe side, I want two."

Here's the question: If, in fact, one plug of grass would give him a lawn in 30 days, on what day must he apply the arrester spray to stop it from subsuming his car, his garage and his kids if he uses two grass plugs?

Last week's puzzler:

You have in your possession two pieces of string, each of which is a couple of feet long. The strings can both be different lengths. It doesn't matter. They�re burnable, like a fuse that�s used to light dynamite.

You could light either end of either string, and it would burn. In fact, if you lit one end of a string, it would burn in exactly an hour.

You light one of the strings with your Zippo lighter. It would burn right along and it would take one hour to be gone.

But here's the wrinkle: the strings do not burn at a constant rate. For example, the string might burn for two minutes and then go crazy and burn like mad, then slow down, etcetera. In other words, you don't know at what rate the string's burning, at any specific time. All you know is that in an hour's time, the whole string is burned. It's not linear, nor is it predictable.

The question is, with the Zippo lighter and these two strings, how would you measure 15 minutes of time?

Last week's puzzler answer:

So, you take String A, light both of its ends. You take String 2, and light one end. Well, what's going to happen? Because you lit both ends of the first string, in a half an hour's time, that string is going to burn up completely. A half an hour has gone by, and similarly, the other string you lit is going to burn for: half an hour's time.

At which point, as soon as the first string has burned up completely, you'll light the remaining end of String 2, and because the first part of that string you lit is continuing to burn, it's going to take 15 minutes before those two flame fronts meet, and you'll have measured 15 minutes from the time that you lit the second string.

So, the question could have been, how would you measure 45 minutes? Or 15 minutes, and it would be the same answer.

_______________________
Scott MacLean
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http://www.nerosoft.com