Self Describing Numbers

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There are several so-called "self describing" or "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 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;

Self-describing numbers < 100,000,000 are: 1210, 2020, 21200, 3211000, 42101000.