There are several so-called "self-describing" or "[[wp:Self-descriptive number|self-descriptive]]" integers.

An integer is said to be "self-describing" if it has the property that, when digit positions are labeled 0 to N-1, the digit in each position is equal to the number of times that that digit appears in the number.

For example,   '''2020'''   is a four-digit self describing number:

*   position   0   has value   2   and there are two 0s in the number;
*   position   1   has value   0   and there are no 1s in the number;
*   position   2   has value   2   and there are two 2s;
*   position   3   has value   0   and there are zero 3s.

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Self-describing numbers < 100.000.000&nbsp; are: &nbsp; &nbsp; 1210, &nbsp; 2020, &nbsp; 21200, &nbsp; 3211000, &nbsp; 42101000.


;Task Description
# Write a function/routine/method/... that will check whether a given positive integer is self-describing.
# As an optional stretch goal - generate and display the set of self-describing numbers.


;Related tasks:
* &nbsp; [[Fours is the number of letters in the ...]]
* &nbsp; [[Look-and-say sequence]]
* &nbsp; [[Number names]]
* &nbsp; [[Self-referential sequence]]
* &nbsp; [[Spelling of ordinal numbers]]
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