PROBLEM: Find a 10-digit number, where the first digit defines the count of zeros in this number, the second digit the count of number 1 in this 10-digit number, and so on. At the end the tenth digit expresses the count of the number 9 in this 10-digit number.

SOLUTION: I solved this by breaking the problem into pieces.

1st – Find a 10 digit number so:

2nd – Where the first digit defines the count of zeros. So lets count how many zeros there are. 10 right not really because the first number represent the number of zeros so there is nine and the new number is:

3rd – the second digit the count of number 1 in this 10-digit number, and so on. This means that the second number represent how many ones there are, the thrid number how many twos there are, the fourth number how many threes and so on. Since nothing matches this rule on to the next.

4th – At the end the tenth digit expresses the count of the number 9 in this 10-digit number. Since there is one number nine in this digit the new number is:

Let’s remember part three. Since there is a number one in our number we need to replace the second digit with the count of number ones. So you might expect this at first:

but now there is two ones so the number is:

The third rule apply again with the third digit representing the count of twos:

Let’s look at rule one the first digit represents the number of zero in our number. That has changed to a six and since rule four say it represents the number of nines this becomes a zero.

Almost done…We have to apply rule three again where the seventh digit represent the count of sixes. so our final step is: