TFA will inform you of this though, it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments first

> it's intended to be a game of reasoning. Posting the answer is spoiling the fun for people who read the comments

This is a very common example in math classes, though in my experience usually presented as a proof that "all horses are the same color".

All cats have nine tails...

No cat has eight tails, and every cat has one more tall than no cat. Ergo...

Why isn't there a mechanism for hiding spoilers in your comments? I came to the comments to check whether my guess was right (it wasn't), and I'm very glad for the spoiler.

You don't need to come to the comments to check your guess, the website lets you check your guess yourself by clicking on the step.

> See if you can figure out in which step the fallacy lies. When you think you've figured it out, click on that step and the computer will tell you whether you are correct or not, and will give an additional explanation of why that step is or isn't valid.

Perhaps downvoted for spoiling the problem? Some people review the comments before looking at the article.

There is a problem in step 9, but the problem is not related to introducing a third person. The existence of a third person makes step 9 correct.

The problem is that we establish the base cases S(0) and S(1), and then we establish the inductive step S(n) -> S(n+1) subject to the restriction that n > 1. But this proof never demonstrates that S(1) implies S(2). The proof is completely correct that S(2) implies S(3), S(3) implies S(4), and so on.

When step 9 says "Let R be someone else in G other than P or Q", the existence of a person in G other than P or Q has not been demonstrated. G is an arbitrary group of k+1 people, and the highest k for which our statement is known to be true is 1. Thus, the minimum size of G is 2, and R may not exist.

I think they mean, introducing a third person into the problem scope. Not into the set G.