A number theory problem by Jasveen Sandral
Number Theory
Level
3
Can you find a seven digit number which describes itself. The first digit is the number of zeros in the number. The second digit is the number of ones in the number, etc. For example, in the number 21200, there are 2 zeros, 1 one, 2 twos, 0 threes and 0 fours.
The answer is 3211000.
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1 solution
We can guess exactly there is no digit 4, 5, 6 and 7. Since if the number of a digit are 4 or more, there are no possible combination. So, try 3 digits of zero. Then the number will be 3 _ _ 1 0 0 0, because there is a digit 3, then in 4th place must be 1. Next, there is a digit 1 in 4th place, its impossible digit 1 in 2nd place. It must be 2 in 2nd place and 1 in 3rd place.