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The number 4 can be expressed as the sum of one or more natural numbers in eight different ways if order matters:

 

 4   1+3   2+2   3+1   1+1+2   1+2+1   2+1+1   1+1+1+1 

 

How many expressions are there for the number 7?

 Apr 13, 2019
 #1
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+1

7 = 7...........................................1
6 + 1 = 7.....................................2
5 + 2 = 7.....................................2
5 + 1 + 1 = 7...............................3
4 + 3 = 7.....................................2
4 + 2 + 1 = 7...............................6
4 + 1 + 1 + 1 = 7.........................4
3 + 3 + 1 = 7...............................3
3 + 2 + 2 = 7...............................3
3 + 2 + 1 + 1 = 7........................12
3 + 1 + 1 + 1 + 1 = 7...................5
2 + 2 + 2 + 1 = 7.........................4.
2 + 2 + 1 + 1 + 1 = 7..................10
2 + 1 + 1 + 1 + 1 + 1 = 7.............6
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7.......1
                                           Total =64 arrangements.

 Apr 13, 2019
 #2
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+1

7                        1  way

6, 1                    2 ways

5,2                     2 ways

4,3                     2 ways

5,1,1                  3 ways

4,2,1                  6 ways

3, 3, 1                3 ways

3,2,2                  3 ways

4,1,1,1               4 ways

3,2,1,1              12 ways

2,2,2,1               4 ways

3,1,1,1,1            5 ways

1,1,2,2,1           10 ways

1,1,1,1,1,2         6 ways

1,1,1,1,1,1,1      1 way

 

So

 

64 expressions

 

cool cool cool

 Apr 13, 2019
edited by CPhill  Apr 13, 2019
 #3
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Thank you! really appreciate it

 Apr 13, 2019

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