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View Full Version : OT - Remember CarTalk and the Tappet Brothers' Puzzlers?



lynnl
07-22-2019, 12:08 PM
I haven't listened to NPR for some time; don't know if they're still re-running those old CarTalk shows.
But I still get weekly emails with puzzlers. In addition to an entertaining challenge, at times they can be good for a laugh. Here's one from this week that hit my "giggle bone:"
(quote)

Give Them the Boot!

RAY: In a country far, far away, there are the two towns of Cityville and Townberg, a few miles apart on either side of a mountain. The preferred footwear in this region is the combat boot.

There are 20,000 people who live in Cityville. And 1 percent of them have one foot only, so they wear, what? One boot. Half of the remaining people in the town wear no boots at all. They go barefoot.

The rest of the people wear two boots. Now you can figure out how many boots there are in Cityville.

In Townberg, 20 percent of the people have one foot. Of the remaining people, half of them wear no boots and half of them wear two boots -- and there are 20 thousand boots worn in Townberg.

Here’s the question. What's the population of Townberg?
(end quote)

Bob Engelhardt
07-22-2019, 12:24 PM
Cityville has nothing to do with the answer.

It doesn't say that the one-footed 20% of Townberg wear one boot, so assume that they don't. Of the remaining 80%, 1/2 (40%) wear 2 boots. 20,000 boots (10,000 pairs) are worn by 40% of population. Therefore there are 25,000 people there.

mklotz
07-22-2019, 12:27 PM
I haven't listened to NPR for some time; don't know if they're still re-running those old CarTalk shows.
But I still get weekly emails with puzzlers. In addition to an entertaining challenge, at times they can be good for a laugh. Here's one from this week that hit my "giggle bone:"
(quote)

Give Them the Boot!

RAY: In a country far, far away, there are the two towns of Cityville and Townberg, a few miles apart on either side of a mountain. The preferred footwear in this region is the combat boot.

There are 20,000 people who live in Cityville. And 1 percent of them have one foot only, so they wear, what? One boot. Half of the remaining people in the town wear no boots at all. They go barefoot.

The rest of the people wear two boots. Now you can figure out how many boots there are in Cityville.

In Townberg, 20 percent of the people have one foot. Of the remaining people, half of them wear no boots and half of them wear two boots -- and there are 20 thousand boots worn in Townberg.

Here’s the question. What's the population of Townberg?
(end quote)

20000*0.01 + 20000*0.99*0.5*0 + 20000*0.99*0.5*2 = 200 + 0 + 19800 = 20000 boots in Cityville

X*0.2*1 + X*0.8*0.5*0 + X*0.8*0.5*2 = 20000
X*(0.2 + 0 + 0.8) = 20000
X = 20000 population of Townberg

tomato coupe
07-22-2019, 01:06 PM
No equations needed. 20,000 boots => 20,000 people.

lynnl
07-22-2019, 05:53 PM
Cityville has nothing to do with the answer.

It doesn't say that the one-footed 20% of Townberg wear one boot, so assume that they don't. Of the remaining 80%, 1/2 (40%) wear 2 boots. 20,000 boots (10,000 pairs) are worn by 40% of population. Therefore there are 25,000 people there.

I dunno Bob, if a person only has one foot I'd think he or she would want to give it as much protection as possible; so I think we ought to assume the one-footers do wear a boot. :)

That's the assumption I made, so I came out with the same result as Mklotz. But I confess I didn't give any thought to the alternative possibility that you arrived at. Possibly because I was distracted, wondering just how in the world 1/5th of a population ends up one-footed. I guess we'll have to assume they let their kids play with lawn mowers at an early age, and probably the rough and rocky terrain on the side of the mountain leads to a lot of tipovers and accidents.

ed_h
07-22-2019, 08:35 PM
Right. No equations necessary. The 20% have 1 boot each, the rest average one boot each.

So one boot per person in Townberg, on average.

Ed