12
$\begingroup$

... in which you have nothing to do with math
... except maybe with some counting and this and that
... but no calculations, no, definitely no.

$1, 0, 8, 62, 90, 68, 83, 89, 88, 057, 619, 028, 693, 069, 068, 985, 086, 988, 871, 820, 838, 865, 890, 868, 887, ?, ?, ?, ...$

Question:

What are the next elements?

Hint 1:

4 is missing for reasons.

Hint 2:

4 is too much.

Hint 3:

4 is somehow ambiguous.

$\endgroup$
15
$\begingroup$

The next numbers are:

$889, 888, 0123$

Because

they are ternary representations of the natural numbers starting at $0$, where the trits are the number of holes in the base $10$ digits
The next ternary numbers to represent are $221, 222, 1000$.
You are cycling through $(0,6,9)$ for those with one hole,
through $(1,2,3,5,7)$ for those with no holes,
with just $8$ for two holes.

$4$ has a hole so it could be used but you decided not to do so because it may also be written without one
($0$ could be written with a slash through it too, giving it two holes).

$\endgroup$
  • $\begingroup$ Well... half way done. Probably because of my fault with exchanged elements (sorry for that). Answer is unambiguous, so... Well done so far :) $\endgroup$ – kamenf May 22 '16 at 1:51
  • $\begingroup$ @kamenf I updated it to use the rest of the methodology I believe $\endgroup$ – Jonathan Allan May 22 '16 at 1:59
  • $\begingroup$ Now it is perfect. And about 0... well, when I was at school there was no such thing as slashed zero, so I totally forgot that case :-D $\endgroup$ – kamenf May 22 '16 at 2:04
  • $\begingroup$ Yeah, it does not matter really, just thought I'd pop that in there - you are writing the numbers after all :) $\endgroup$ – Jonathan Allan May 22 '16 at 2:07
  • 1
    $\begingroup$ @warspyking I don't think any conversion (ether from ternary to decimal or vice-versa) is needed to solve this puzzle. Even to present them as text. Just digits. :) $\endgroup$ – kamenf May 22 '16 at 19:36

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.