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More Referential Numbers (Posted on 2005-12-10) Difficulty: 4 of 5
Numbers like 21200, 3211000, and 6210001000 are self referential numbers, where the first digit is the number of zeros in the number, the second digit is the number of ones, etc. These were presented in the Self-Descriptor problems.

There are also pairs of numbers like {230100, 311100} which are cross referential numbers, where the first digit of one number is the number of zeros in the other number, second digit of one number is the number of ones in the other number, etc. By length, {230100, 311100} is the smallest such pair. Can you find longer cross referential numbers?

There are also cyclic referential numbers like the set {4110100, 3300100, 4102000}. 4110100 describes 4102000, 4102000 describes 3300100, and 3300100 describes 4110100. Are there any other cycles?

No Solution Yet Submitted by Brian Smith    
Rating: 4.0000 (2 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
the coolest referential number is 2020tanx2005-12-28 19:06:47
Hints/Tips16-digit exampleMindRod2005-12-11 13:12:31
Hints/TipsOne longer number and some thinking...Eric2005-12-10 19:34:33
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