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The kids were discussing fiercely during the school break (ah, those were the times!). The subject: Bragging about who can count up to the highest number.

John said "I can do 20". Jolene said "I know up to 50!". Miles said "I know up to a hundred!".

Little Marie felt sad, she was the youngest and not only had she studied only up to 10, but she was bad at it too. To her great gladness, at that time, her cousin, a science university grad, just strolled up to say hi!

"Big Cousin Nicola, please tell us how high you can count"!

"Well Marie, I'll tell you a more interesting thing instead - I know a number that can itself count"!

What is that number?

Hint:

The associated knowledge science is not math. Also, no lateral thinking (at least on word level).

Hint2:

The associated knowledge is not programming. Else, any program that implements counting could be interpreted as a number and be the solution.

Hint 3(strong):

3 digits

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    $\begingroup$ It seems to me that without the hints, this question is not well-defined enough. Which means the hints aren't really hints. They're vital parts of the puzzle. $\endgroup$
    – bobble
    Jan 12, 2021 at 19:09

9 Answers 9

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This is a stupid answer I spent way too much time searching for. I know this isn't the answer.

It is of course

4308900011000

because

When using this number as the source code in the well-known and respected esoteric programming language Numeric Topline, the program just counts from 1 up to infinity! (well, not really. Probably up to 2^31-1).

The instructions are:
43 - Reset the count to 0. Solely here because the number (source code) itself can't start with a 0
08 - Start of an infinite loop
90001 - Add 1 to the count. +- determined by set polarity, which is positive by default. Count is 0 by default, so we start at 1 after this instruction.
10 - Print out the current numeric count
00 - Marks the end of the loop. Not meaning the program stops there, just that everything between 08 and 00 is looped forever.

Side note

First number 43 can of course be replaced with other statements that do nothing in our context, like 47, which sets the polarity to positive (which it already is by default)

Furthermore, if we use ASCII-output instead of numerical and "create" the numbers with ASCII by ourselves, we could make this program count much higher. But I can't be bothered for obvious reasons.

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I'm going to guess that what you're thinking of is

The Champernowne Constant

Reasoning

The number is obtained by concatenating the decimal representation of successive integers after the decimal point so, in a way, it represents counting. Also, it is known to be transcendental.

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  • $\begingroup$ Nice one. Added a hint explaining why it's not. $\endgroup$
    – George Menoutis
    Jan 12, 2021 at 16:51
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    $\begingroup$ If you have to add a "hint" to invalidate an answer, that's a clarification, not a hint. $\endgroup$
    – bobble
    Jan 12, 2021 at 19:26
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A self-descriptive number counts its digits.

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  • $\begingroup$ Nice try, but looking for a more general count. $\endgroup$
    – George Menoutis
    Jan 12, 2021 at 18:09
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This is a really weird guess, but

315211420

Explanation:

It is A1Z26 for "count".

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  • $\begingroup$ Shucks, why did this recieve a delete vote? $\endgroup$
    – new Q Open Wid
    Jan 12, 2021 at 17:04
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My answer:

128

Explanation:

128 is rebus for "One to infinity".

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Four as it counts four letters? (as the only one between 1 and 10)

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  • $\begingroup$ "it counts 4 letters"? $\endgroup$
    – new Q Open Wid
    Jan 12, 2021 at 16:34
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Perhaps the answer is

123

Since if you say the digits aloud,

one, two, three ... it sounds like counting

Why not

1234 ?

Because of the third hint, and of the way children describe counting.

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My answer is:

212

This is because

The number is 2, and it counts itself: 1, 2.

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My guess:

121

Because it is

1 2, and 2 1's

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