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Digit equivalence (Posted on 2021-06-22) Difficulty: 3 of 5
Consider the set S of all integers between and including 1000 and 99999. Call two integers x and y in S to be in the same equivalence class if the digits appearing in x and y are the same. For example, if x=1010, y=1000 and z=1201, then x and y are in the same equivalence class, but y and z are not. Find the number of distinct equivalent classes that can be formed out of S.

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): solution | Comment 3 of 5 |
(In reply to re: solution by Kenny M)

While 100 is out of the range, there are several that are within range:


{1000, 1001, 1010, 1011, 1100, 1101, 1110, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101}

This is one of the C(10,2)=45 equivalence classes in my solution, the 2 chosen in this particular case being 0 and 1. In fact this is the equivalence class to which x and y are members in the statement of the problem.

Edited on June 22, 2021, 6:02 pm
  Posted by Charlie on 2021-06-22 17:58:52

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