An autobiographical number is an integer with at most 10 digits such that the leftmost digit of the number counts the number of 0s in the number, the second digit from the left counts the number of 1s, and so on.(a) Find an autobiographical number

(b) Find the smallest autobiographical number.

Source: 1995 PEI Math Competition

For a fairly complete, short construction of autobiographical sequences (= curious sequences) see: MATH. MAG. 66:4 (October, 1993) p. 276. You can find related references there. (Courtesy Chris Fisher and Stan.)

© Copyright 1999 Rob Leduc. Reproduced with permission.

17 March 1999