Bertel Lund Hansens hjemmeside

Autobiographic numbers

1210
2020
21200
3211000
42101000
521001000
6210001000

This is how far you can go with decimal numbers. A digit on the 11th position makes no sense.

If, on the other hand, you accept bases greater than 10, the following numbers are possible:

821000001000
9210000001000

and if you accept digits greater than 9, there is no limit:

A2100000001000
B21000000001000
...

Haven't you guessed the system yet? Take 1210. It has 1 zero, 2 ones, 1 two and 0 threes - 1 2 1 0.

Couldn't we just drop the last zero? Or set one more zero? After all there are no fours.

No, we couldn't. The first digit specifies the number of zeroes, and 121 has no zeroes.