### Logic Puzzles #2 - Responses

OK, here are the responses to the logic puzzles from Friday:

1) You are tempted to say the difference is miniscule since only one yard (36 inches) was added over 25 thousand miles of circumference. However, the ratio between the diameter and circumference of any circle is a constant; namely "pi", which ~=3.14. Therefore, if you add 36 inches to the circumference of the string, the diameter goes up by about 11.2 inches (=36/pi). Therefore, at every spot all around the earth the belt can now be raised by ~5.6 inches.

2) As David implies with his Trek reference in the comments section, the answer to both this and #3 is based on exponential growth. In this case, the final wad of paper would be 2 to the 50th power, or about 1.1 quadrillion sheets thick. Assuming about 100 sheets to the inch, the total stack would thus be about 177 million miles thick, or almost twice the distance from the earth to the sun. Of course, in practice it's impossible to fold a piece of paper more than nine or ten times. Believe me, I've tried!

3) This can be solved on paper using logarithms, but to spare all the formulae, the answer is about 10 to the 40th power dollars, which is way more than the value of the entire earth and all its possessions. In fact, it would be enough to buy several hundred thousand globes the size of the earth made of solid gold. Too bad our ancestors at the time the mishnah didn't think to invest a zuz or two, instead of spending them all on goats!

4) David gave the answer to this one - since it doubles each day, it covers half the lake in 29 days, so two of them would take 29 days to cover the entire lake.

5) The obvious answer would be that he can make two cigarettes with eight ends, and will have three ends left over. In fact, he can actually make three cigarettes and have two ends left over when he finishes. As follows: he makes the first two cigarettes out of the first eight ends, then he smokes those, and uses one of the two ends from those cigarettes to make another cigarette with the original extra three, which he then smokes, leaving two ends left over!

## 1 Comments:

That's 28 days.

Was that typo another puzzle?

:-)

BTW, after the other poster wrote 2 cigarettes with 3 butts left over I realized what the answer was.

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