Car Talk's puzzle of the week: impossible?

Some friends of mine were visiting from out of town, and we went to a local botanical garden - as we were walking up the internal spiral staircase of a stone observation tower my friend made a comment about the tower’s construction which I thought could be a good basis for a puzzle. I sent in my experience - “what did my friend mean?” - here’s what aired after obfuscation:

I’ve actually heard that one twice - they recycled it when the Puzzler was on vacation last summer.

This puzzle is originally from 2003. I did a search and found this:

They apparently took that offline after you found it. But Google still has a cache. And, as I predicted but apparently forgot to post, the correct solution is in this thread, and does not involve 3-cent pieces.

So I posted the correct answer but I was still wrong because I thought that I had solved the puzzle as posted by the OP.

As posted by the OP, the answer involving 3 cent pieces works. Actually it also works for the original wording, both mathematically and because vending machines won’t take 3 cent pieces. It’s just not the solution they were looking for.

A dollar coin, a dime, a nickel, and three foreign coins of your choice.

I’m happy there’s a less bogus answer to the puzzle than the one I came up with…

After looking at the solution, what’s interesting is that if the staircase was enclosed (with walls on both sides), the opposite would be true (and it would matter more).

I don’t understand the solution to the tower puzzle. They seem to have it backwards. The medieval towers had it spiraling counter-clockwise, not clockwise, as they say. The incorrect tower would be clockwise, not counter-clockwise, as they say.

If I was at 6 o’clock and was running up to the 3 o’clock position, that’d be good for me and bad for the defender. That direction is counter-clockwise.


Nope. It spirals UP clockwise, so that the defenders at the top have the advantage.

Dammit. I screwed it up while typing it. Here’s what the website says:

I typed it wrong initially, saying they said the opposite of what they did say. But just to be clear, I’m claiming that this is incorrect. Towers, when viewed from the base of it, go clockwise. They’re saying it goes counter-clockwise in the bolded part.

It sounds like we’re in agreement that the site is wrong.

The real error is that nobody would describe the staircases from the bottom. You visualize it from the top. I think he just misspoke when he said “viewed from the bottom.”

I visualize it from the point-of-view of the narrator. In this case, that’s a dude standing on the ground several hundred yards away, and I’d definitely visualize it from the ground up.

I was thrown by the point about the “inside wall”. In describing a stone tower, that can refer to at least two different places, depending on how it’s constructed.