A pattern of grouping nonnegative integers into certain sets

[lookagain]

This problem of mine is flawed from the outset, because there
can be an unlimited number of ways to answer it, and then
you could get credit regardless if your support your answer
with a valid reason.

Suppose you are attempting to pick out my intended rule.
What is the pattern for how these numbers are put in
their respective sets?

Note: Because they are sets, the order of the numbers
shown in any set does not matter toward the pattern.


\(\displaystyle \{1, 2, 6, 10\}, \{0, 4, 5, 9 \}, \{3, 7, 8, 40, 50, 60, \}, \{11, 12, 20, 30, 80, 90\}, \{15, 70\}, \{13, 14, 18, 19\}\)

 

[soroban]

Re: A pattern of grouping nonnegative integers into certain

Hello, lookagain!

What is the pattern for how these numbers are put in their respective sets?

\(\displaystyle \begin{array}{c}\{1, 2, 6, 10\} \\ \{0, 4, 5, 9 \} \\ \{3, 7, 8, 40, 50, 60\} \\ \{11, 12, 20, 30, 80, 90\} \\ \{15, 70\} \\ \{13, 14, 18, 19\}\end{array}\)

You missed a few . . .

\(\displaystyle \begin{array}{c}\{1, 2, 6, 10\} \\ \{0, 4, 5, 9 \} \\ \{3, 7, 8, 40, 50, 60\} \\ \{11, 12, 20, 30, 80, 90\} \\ \{15,16,70\} \\ \{13, 14, 18, 19, 41,42,46,51,52,56,61,62,66\} \\ \{17,21,22,26,31,32,36,44,45,49,54,55,59,64,65,69,81,82,86,91,92,96\} \\ \{24,25,29,34,35,39,43,47,48,53,57,58,63,67,68,71,72,76,84,85,89,94,95,99\} \\ \{23,27,28,33,37,38,74,75,79,83,87,88,93,97,98\} \\ \{73,77,78\} \end{array}\)

[spoiler:25cxjhps]The numbers are written in words (in English).
Then the numbers are grouped by the number of letters in each name.

3 letters: {one, two, six, ten}
4 letters: {zero, four, five, nine}
. . . . . and so on.

I assume the numbers are integers from 0 to 99, inclusive.[/spoiler:25cxjhps]

 

[lookagain]

Re: A pattern of grouping nonnegative integers into certain

You missed a few . . .

No, I didn't because...
[spoiler:1hljhp1j]I deliberately used numbers which do not have hyphens in their spellings,
as hyphens add another character. My numbers do not have hyphens in their
spellings. There is no ambiguity, then, as to counting letters or counting all
characters used for the spellings of the numbers. I chose 26% of the integers
from 0 to 99 (inclusive) on purpose to place among the sets.[/spoiler:1hljhp1j]


Part of soroban's spoiler:
[spoiler:1hljhp1j]The numbers are written in words (in English).
Then the numbers are grouped by the number of letters in each name.[/spoiler:1hljhp1j]