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A is the set of all numbers with four digits that can be created with odd numbers! Example: [1111] [1,3,5,7] belongs to A.

xRy if and only if the sum of the four numbers that x have is the same sum of yś four digits! Example: [1,3,5,7]R[9,1,3,3]

How many equivalence-relations exist and how many elements exist in the class [3997]

My thoughts! For the first, I have no clue hot to do on the first question. But We have 5 numbers that we can use(1,3,5,7,9)! But I really don´t know what to do :(

Second question: Well the sum of the numbers on that class is 28 so I guess I should find others with the same sum, is that correct!

I found this: [3997] = [ 7777] = [5779] = [1999] = [5599]

And now? :(

Bojack
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1 Answers1

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Hint. For the first question, each equivalence class is indexed by the sum of the digits of any of its members. How many possible sums are there? For the second, brute force will work (save yourself some brute by noting that any permutation of a number is in the same equivalence class).

Tony Huynh
  • 872
  • Question:1 The lowest sum is 41 and the hight is 49 So that is 36-4 = 32! But we can´t get any odd sums so it should be 32/2 = 16!

    Question:2 Ok..So their is not any good general method? Thanks alot!

     – Bojack Aug 15 '13 at 12:18
  • That's close, but not quite right. – Tony Huynh Aug 15 '13 at 12:21
  • Yea I did it by hand and it´s 17 not 16! 0-16 is 17 numbers, I didn’t include the first one, is that correct? – Bojack Aug 15 '13 at 12:27
  • Its funny! I get one to much on question number2! My paper has 34 as an answer and I have 35! Looks like the don´t have [7777] as an element! But why? – Bojack Aug 15 '13 at 12:46
  • Well, the Paper or the Man is not always right. Question authority. – Tony Huynh Aug 15 '13 at 13:24