Absolutely true.

If you take a look at the wikipedia link that tommy posted above, you'll see that there's a fair amount of discussion about the proper formulation of the question.

As I'm very familiar with the problem, I know that your interpretation is not what the problem solver intended. I'm not saying that your interpretation is unreasonable by any means; only that that's not what was intended.

Hi $2000magician,

It’s not the first time I’ve interpreted things differently than others I’ve enjoyed the mental exercise... thanks

Regards, Steve

Such as my username.

It's S2000 (as in Honda's incredible roadster), not $2000.

LOL! Sorry about that (and I got it right the first time, but thought I had made a mistake). Maybe it's time for new glasses

Regards, Steve

Then you know whether it's the older penny (the wheat penny) or the younger penny (the Lincoln Memorial penny).

See: you're using older and younger even with your pennies.

There probably aren't many on this forum that remember wheat pennies

Regards, Steve

Never mind pennies, I remember farthings.

I remember penny-farthings.

I own one.

I remember wampum and trading five Eddie Kranepools for one Micky Mantle.

Is the small wheel a 1/4 of the big wheel?

Even smaller.

I'll measure them and get back to you with a concrete answer.

About ⅓ the diameter, so 1/9 the area (when viewed sideways).

A farthing was a ¼ of a penny in value - from "fourthing". The pre-decimalisation British system of coinage was introduced by King Henry II. It was based on the troy system of weighing precious metals. The penny was literally one pennyweight of silver. A pound sterling thus weighed 240 pennyweights, or a pound of sterling silver.

From what I've looked at on Wikipedia, the most recent farthing had a diameter of 20mm and the quarter farthing 13.5 mm. So the area would be about 45% of the larger. The old farthings were as large as 25mm in diameter, which works out to about 29%.

There's nothing like a probability paradox to get me out of a many-years-long spell away from the forum...

Here's a Jedi Grandmaster level probability puzzle:

Suppose I have an everywhere-nonzero probability distribution on the real number line.

If you don't know what that means, in layman's terms it means that I have some probabilistic process or method to generate a random number. It can potentially generate ANY number. Moreover, if you pick any range of numbers, whether the range is large or small, there's a nonzero probability that you can generate a number inside that range. (It may not be obvious, but such things exist.)

But importantly, you don't know anything else about the distribution. You don't know its mean (or if it even has a mean), you don't know if it has any symmetries, you don't know ANYTHING besides the fact that it's everywhere-nonzero.

Then we play a game: I use that secret distribution to generate two distinct numbers, but I don't tell you either number. I then flip a fair coin to decide which of the two numbers to show you.

Upon showing you the number, you're allowed to say "larger" or "smaller." If in fact the number I showed you was larger than the other number (that I didn't show you), you win if you said "larger" and lose if you said "smaller." Similarly, if the number I showed you was smaller than the other number, you win if you said "smaller" and lose if you said "larger."

Obviously, you can't do this with 100% success. That's not the question. The question is whether you can come up with a strategy that's better than merely guessing at random.

For example, one strategy might be to always answer that the number is the larger number. But you'd only be right 50% of the time.

Is there a strategy that provides a better than 50% success rate?

Yes.

Maybe I should have been more clear: if so, what is one such strategy? If not, why not?

Create a random number along the distribution. That will be your comparison value. When you turn over one of the random numbers, you will compare it to your random number. If it is higher, then you will pick "lower" and vice versa. This only gives you a slightly better than 50-50 chance of being right. The reason this works is because in the off chance that you are number lies between the two numbers the other person chose, you will always be right. Otherwise, it is still just a 50-50 chance.

We used to operate a scam on the bookies some time ago. One would place a complicated bet on a large number of football teams and under stake the number of combinations. The bookies would take the bet without checking the number of doubles, trebles, four timers and so on it should be. After they would just look at the winners and settle up. One would perhaps get say a grand bet on for 700. There was no guarantee of winning but it gave one the edge.

Well done, Steven, you are a Probability Jedi Grandmaster!