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Self-Descriptor part 2 (Posted on 2002-10-11) Difficulty: 3 of 5

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.

  Submitted by Happy    
Rating: 3.3333 (6 votes)
Solution: (Hide)

1210

Try to find a number less than 1210: ABCD, or ABC, or AB, or A.

A: Can't be zero. If A >= 3, then the number would have be over 3001 (in order to state that there are at least 1 3's in the number). If A = 2, then to be under 1210, the number would have to be exactly 200 which is not self-describing. Thus, A = 1.

B: Since A = 1, B >= 1. B cannot be 1 because then we'd have 2 1's. if B >= 3, then the number would have to be over 1300. Thus B = 2.

C: Since B = 2, C >= 1. If C = 1, this would fulfill B's count.

D: Since we stated that A is 1, there must be one zero in the number. D = 0 fulfills this condition.

Thus, the smallest self-describing number is 1210.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-03-08 12:17:48
re(2): Solution part 2Happy2002-10-14 05:39:14
re: Solution part 1 (Definitions and rules)TomM2002-10-12 06:35:35
Solutionre: Solution part 2TomM2002-10-12 06:28:04
Hints/TipsSolution part 1 (Definitions and rules)TomM2002-10-12 06:26:19
Solutionre(2): Is this right?Nick Reed2002-10-12 05:26:03
Questionre: Is this right?levik2002-10-12 05:12:42
Is this right?Aeternus2002-10-11 21:47:18
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