Problem 49572. Compute the largest number possible with the Brussels choice

Created by ChrisR

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The Brussels choice (or Choix de Bruxelles) operation changes one number to another by taking a substring of the digits and either doubling it or (if the number is even) halving it. For example, starting with 9 and highlighting substrings, one can generate this sequence:
9, 18, 36, 312, 622, 644, 1288, 1488,...
Another possibility is 
9, 18, 116, 232, 464, 924, 1844, 1888,...
Both of these excerpts have eight entries, but the second ends in a larger number than the first. 
Write a function that takes an initial value  and determines the largest number  resulting after n steps. In the above examples,  = 9 and . Return the number as a character string.

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Last Solution submitted on Dec 16, 2025

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William on 24 Dec 2020

Chris, -- In the first example, is the fourth number supposed to be 312 rather than 112, or am I misunderstanding the description?

ChrisR on 24 Dec 2020

Yes, you're right. Thanks. If you start with 1, you will see why I made that mistake.

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Problem 49572. Compute the largest number possible with the Brussels choice

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Problem 49572. Compute the largest number possible with the Brussels choice

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Last 200 Solutions

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Problem Recent Solvers13

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