A nice number!

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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2 solutions

Ivander Jonathan
Jan 9, 2015

The first digit will be the largest, since we need zeros to fill in the spaces.

Try out different numbers of zeros.

9000000000 9000000000 - wrong, since the tenth digit must be a one.

8000000010 8000000010 - wrong, since the second digit must be a one.

7000000100 7000000100 - wrong, since there are eight zeros.

6210001000 \boxed{6210001000} - the correct answer.

the greedy approach that we fill it with zero so the first number is n>=1 where the digit of n must be 1 so if we put 1 in 1's digit we have find that number of 1's became 2 because it match its position so i have to put in it 2 as i know ,i have to fill 2's digit with 1 so i will have 2 1's which matches the rules .

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