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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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Solution solution | Comment 1 of 5
The set of digits, in most instances, can be the number of combinations of 10 things (the digits) taken 1, 2, 3, 4 or 5 at a time. For example 71803 is in the same class as 30178. The only exception to this is numbers consisting solely of zeros--they are not in the range. The other single-digit classes each have two members, such as {1111, 11111} or {9999, 99999}.

 n      C(10,n)
 1          10 - 1 = 9
 2          45
 3         120
 4         210
 5         252
           ---
           637 - 1 = 636
           
There are 636 equivalence classes.            
 

  Posted by Charlie on 2021-06-22 10:42:59
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