The Two Answers

posted at 5:24 pm
on Dec. 4, 2006

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OK, here’s the answers to the logic questions I asked last week:

If you haven’t seen the questions, check them out first.

Don’t peek!

Ready?

OK, #1 first.

This is a percentages problem and a human perception problem, that comes up with a really counter-intuitive result.  Most people think that, since there are only 15% blue cabs, and since the color is correctly identified 80% of the time, that it’s very likely a blue cab will be properly identified.

But that ignores people trying to identify green cabs.  Here’s the math: if 100 people see 100 cabs, there are going to be 15 truly blue cabs identified.  12 of those blue cabs would identified as blue. (The other 3 would be called green by mistake.)

Meanwhile, of the 85 green cabs, 68 would be correctly identified as green (80%).  The other 17 green cabs would be called blue.  So of the people who said “Hey, that’s blue,” we have 12 correct identifications of blue cabs, and 17 mistaken blue identifications.  12 out of 29 correct, that’s only 41% correct, and a whopping 59% incorrect identifications.

And that’s just one reason why eye witness reports are fairly unreliable.  Mitzy came closest in getting that question correct.

Now, #2.  The secret is, you need to get the ropes mostly all burning at once.  So, fold one of the ropes over, and hold both ends together with one end of the other rope.  Light the stick and then light the three ropes ends at once with the stick.  The first rope is now lit at both ends and will burn up in 30 minutes.

This is called burning the candle at both ends and I am familiar with the technique.

Meanwhile, when 30 minutes have passed and the first rope is gone, the second rope will have burned half way (because it’s only lit at one end).  Put it out.

So you now have left a rope that will take 30 minutes to burn, or 15 minutes to burn if you light both ends. And you can time 15 minutes. Tah dah!

Christina said she’d make a sun dial. Mitzy said she’d look at her watch.  I’d accept both answers, though neither is really the one I was looking for.  And that means MITZY has won the prize.  Send me your address and the book is on its way!

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