Naughts and Ones

[bonanova]

Treating the capital letters as geometric shapes, I classify them as "naughts" and "ones."

The naughts are: ABEFGHKPQRSTXY

The ones are: CDIJLMNOUVWZ

Applying the same assignment rule, if you can discern it, which four of the digits 0123456789 are "ones"?

What is the rule?

[TheCube]

I see multiple patterns in each one.

But something tells me this, I dunno why though:

0,1,2, and 7

[bonanova]

I see multiple patterns in each one.

But something tells me this, I dunno why though:

0,1,2, and 7

Three out of four. Close.

the first two orders of infinity.

Aleph naught (or Aleph null) and Aleph one.

So that's a clue about the rule.

[WitchOfSecrets]

I'm bugged by the following:

S is a nought, Z is a one. This suggests that a rule about curves vs. straight lines is involved. But...

G and Q are noughts; C and O are ones.

All of the ones can be drawn without lifting pencil from paper or retracting steps. Almost none of the noughts can - except for G, B, P and and S.

[bonanova]

I'm bugged by the following:

S is a nought, Z is a one. This suggests that a rule about curves vs. straight lines is involved. But...

G and Q are noughts; C and O are ones.

All of the ones can be drawn without lifting pencil from paper or retracting steps. Almost none of the noughts can - except for G, B, P and and S.

Thinking along the right lines (npi).

How many of each can be drawn on a sheet of paper?

[WitchOfSecrets]

A-ha.

Given a sheet of paper of infinite size and the ability to draw infinitely (trans-finitely) many letters of any size (without rotation), you could fill a sheet of paper with 'one' letters completely, without showing any white space. A second copy of a one letter can be made to fit neatly inside or next to a first copy.

In contrast, no matter how many copies of a naught you put on the page, you will always trap a certain amount of whitespace between them.

So the ones are:

0, 1, and 7. 2 almost works, but not quite. I'm not sure if J is really a one, though.

Edited June 8, 2012 by WitchOfSecrets

[bonanova]

A-ha.

Given a sheet of paper of infinite size and the ability to draw infinitely (trans-finitely) many letters of any size (without rotation), you could fill a sheet of paper with 'one' letters completely, without showing any white space. A second copy of a one letter can be made to fit neatly inside or next to a first copy.

In contrast, no matter how many copies of a naught you put on the page, you will always trap a certain amount of whitespace between them.

So the ones are:

0, 1, and 7. 2 almost works, but not quite. I'm not sure if J is really a one, though.

That's the notion I had in mind.

Nice.

Actually a [finite] sheet of printer paper suffices to show the distinction of the two classes.

Details of the type font come into play, but I think in BD font face only four of the decimal digits are type 1.

Three of yours are in that group.

[Yoruichi-san]

J works as a 'nested' one, you put smaller/larger J's around it. For that same reason, I'm going to guess the last number is 3? It's kinda hard to see with the font, but I think you can nest them inside each other.

[bonanova]

J works as a 'nested' one, you put smaller/larger J's around it. For that same reason, I'm going to guess the last number is 3? It's kinda hard to see with the font, but I think you can nest them inside each other.

That's the right reason and the right answer.

And is the "naught" and "one" distinction evident?

[bonanova]

That's the right reason and the right answer.

And is the "naught" and "one" distinction evident?

Only a countable infinite number of naughts

can be drawn on a sheet of paper.

[Yoruichi-san]

Only a countable infinite number of naughts

can be drawn on a sheet of paper.

Oh yeah, sorry, I wasn't sure what you meant by the question...yes, that was very evident, especially with the aleph hint earlier. Very nice .