The punchline rears its worn out head

Thanks, Quick. Your tip about the single digit number for *c* sent me in the right direction. Actually, I see numerous errors now. I also substituted 16 for *b* in my step 2. And steps 1 and 2 are themselves erroneous. I repeatedly followed Soroban's steps in the order that he presented them in, rather than the order that was intended to be followed.

To solve for *c* we use

where *a* and *b* are any single digits we want to test. We want the result of the test to be a whole number, rather than a fraction. For instance, going through various combinations, if

*a* = 1 and *b* = 2

or if *a* = 1 and *b* = 3

or if *a* = 1 and *b* = 4

and so on, then our formula fails the test. However, if *a* = 1 and *b* = 6, then

and our formula passes the test, because we have a single digit for *c*.

We then apply our solution for *c* to the formula

This formula results in the butt of the joke, because

Which means that

might be an incorrect method of simplifying the fraction, but it certainly does not give the wrong answer.

Another fraction in Soroban's list,

might show an incorrect way of simplifying, but if we solve for *c*

and apply the formula

And so on. Well I really drilled the humor out of the joke, but at least I get the joke now. :)

Don't all clap at once. :rolleyes: