In Self-Descriptor, we found a number ABCDEFGHIJ such that A is the count of how many 0's are in the number, B is the number of 1's, and so on.
I wonder... what if the number didn't have to be 10 digits long?
Find the smallest whole number such that the left-most digit describes the number of 0s in the number, the next digit describes the 1s, etc. Prove that it's the smallest.
(In reply to
Solution part 1 (Definitions and rules) by TomM)
The only describable number of one digit is 0 (rule 1). Its descriptor is 1, so it is not a self-descriptor.
The only describable numbers of two digits are 00, 01, 10 and 11. Only 11 follows the other two rules. Its descriptor is 02, so it is not a self-descriptor.
The three digit describable numbers that also follow rules 2 and 3 (and their descriptors) are 102(111), 111(030), 120(111), 201(111), and 210(111). None are self-descriptors.
The 4-digit numbers that follow all three rules are : 1003(2101), 1012(1210), 1021(1210), 1030(2101), 1102(1210), 1111(0400), 1120(1210), 1201 (1210), 1210(1210)*, 1300(2101), 2002(2020), 2011(1210), 2020(2020)*, 2101(1210), 2110(1210), 2200(2020), 3001(2101), 3010(2101) and 3100(2101). There are two self-descriptors: 1210 and 2020. So, 1210 is the smallest possible self-descriptor
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Posted by TomM
on 2002-10-12 06:28:04 |
re: Solution part 2
