A nine digit number has the property where the first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, the third digit equals the number of twos and threes used in the number, etc. through the ninth digit equals the number of eights and nines used in the number. What could the number be?

A ten digit number has a similar property to the nine digit number. The first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, etc. through the ninth digit. And also, the tenth digit equals the number of zeros and nines used in the number. What could this number be?

a) 740110110

b) 4224400004

For (a), create a string of 9 zeroes. Below it, write out a string of digits representing the number of digits in the above number that correspond to the place in the current number. So for example:

000000000
900000000
900000001
910000001
920000001
921000001
831000001

... and so on. Continue this process until you get a repeat of the line above, and that's your number.

For the 10 digit version, you need to start with something else, like 8000000008, since if you start with all zeroes you will have 10 zeroes.

Posted by Avin on 2005-09-23 18:57:52