Still think the existing answer is right that the black dot is their and there is no solution. But I'm done bothering with it.

There*

yeah, edderiofer's point is that emma's answer may or may not be correct, but it's not a COMPLETE solution. a COMPLETE solution would include a more rigorous proof

I'm with you tho. Rigorous proofs don't particularly interest me.

Proofs at all don't interest me and bother me more than they should.

I don't at all claim to be the smartest person here. But insinuating I'm incompetent 🤔 K.

it's very easy to non-rigorously "prove" something false.

what bothers you about them?

which is why we have rigorous proofs

like, being asked to provide a rigorous proof as if you're still in school is bothersome? Or the idea that we need them at all is bothersome to you?

When you say X = 5. And say now prove it, my question is why.

That's what bothers me.

For things we don't know are true, I guess you can use them. But I don't think mathematical proofs are the only way to determine things.

There are two reasons

1) The person asking is a teacher, and wants you to learn how to prove things (in case you need to prove something you do not know is true in the future)

2) The person asking is asking for the same reason you would ask someone to solve a puzzle you already know the answer to (i.e. they think it's a fun exercise)

Both of which I dislike in this sense.

if you disliked 2, you wouldn't be here in Puzzling.

yeah I never enjoy the activity of being asked to prove something. I just steer clear of those 'proof' questions on this site

(you may disagree that it's fun, sure; but not with the general principle of answering challenges for fun)

@ffao not necessarily

To me this one's a mathematical proof and asking for someone to disprove 2^98 possibilities

and disproving 2^98 possibilities makes it not a challenge because...?

I'm not a computer and allowed to make generalizations

(why did I peek here again on my way out the door?)

@humn peek-a-boo

yeah, n_p's disliking of proofs is preventing him from being rational on this matter

Computers of the future will be full of inaccuracies, but the numbers of correct pathways will make that inconsequential.

of course you're not intended to eliminate all 2^98 possibilities by hand, that is the challenge

I don't think I'm being all that irrational

Rationality is just a frame of mind.

The CCCC archive hasn't been updated in a couple clues

If I was irrational I'd delete my SE accounts... Not a bad idea either

@MorganG I haven't touched it in a couple clues and not many others have been updating it