10-digit Number Puzzle
Level
2
Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.
The answer is 6210001000.
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Let there be n number of zeroes so (n+1)th digit is 1. Now 2nd digit cannot be 1 as then number of 1's would be 2 so 2nd digit would be 2. This means 3rd digit is 1(as there is a single 2) so our number looks like : n21 followed by all zeroes except the (n+1)th digit which is 1. the number of zeroes can now easily be counted to be 6 and hence the 7th digit is 1. the solution thus being 6210001000