Self describing numbers!
The number 521001000 is a number that describes itself because the digits represent the number of occurrences of each digit specified. That is, 5 represents the number of zeroes, 2 represents the number of ones, and so on.
Another example of this number would be 3211000 which has 3 zeroes, 2 ones, 1 two, and so on.
What is the smallest number that exhibits this property?
The answer is 1210.
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The desired number must contain at least one 0 , since we can't have the number starting with a 0 . If we then have one 0 , the second digit cannot be 0 , since we have one 1 already, and it can't be 1 either, since we would then already have two 1 's.
If the first two digits are then 1 2 , the third digit cannot be 0 , since we already have a 2 . So in order to have one 0 we must place it as the fourth digit, leaving us with 1 2 1 0 as the smallest self-describing positive integer.