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Shrinkable numbers (Posted on 2011-04-05) Difficulty: 3 of 5
A shrinkable number is one that can be reduced to a single digit by the following process:

Create a new number where each digit is the absolute difference between consecutive digits.
Repeat until you have a single digit.
No digit is allowed to be a zero at any point in the process.

7624 is shrinkable. It reduces to 142 which reduces to 32 which reduces to 1.
4131 is not shrinkable because it reduces to 322 which reduces to 10 which contains a zero.

Your goal is to create the smallest possible n digit shrinkable number for n = 2, 3, 4, ...
Is there a shrinkable number for any value of n?

No Solution Yet Submitted by Jer    
Rating: 5.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutioncomputer solutionCharlie2011-04-05 18:18:26
Solutionre: answerCharlie2011-04-05 18:13:00
SolutionanswerDej Mar2011-04-05 15:19:39
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