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How many ways can you find whole numbers adding up to five if the order matters? [So 1 + 4 and 4 + 1 count as two

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How many ways can you find whole numbers adding up to five if the order matters? [So 1 + 4 and 4 + 1 count as two different ways or   3+ 1 + 1 and 1 + 3 + 1]. Even though there's no actual addition involved we'll count 5 by itself as 1 way. This is a bit of a weird thing to do but mathematicians do this sometimes and it will make more sense later.

Technical point: actually 0 is a whole number so I should have said whole numbers greater than 0 (that is: 1, 2, 3, etc). These are called the Natural numbers.

Jun 20, 2018

#1
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so, 0 is a whole number

5,0

4,1

3,2

2,3

1,4

0,5

so 6 ways

Jun 20, 2018
#2
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Partitions of (5) = 7  [This is called the "Partition Function"]

5 = 5
4 + 1 = 5
3 + 2 = 5
3 + 1 + 1 = 5
2 + 2 + 1 = 5
2 + 1 + 1 + 1 = 5
1 + 1 + 1 + 1 + 1 = 5

You can put them in any order you want, such as: 1+1+3, 1+3+1, 3+1+1.....etc., and then count them.

Jun 20, 2018
edited by Guest  Jun 20, 2018
edited by Guest  Jun 20, 2018
#3
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oh c**p you're right. I forgot about that.  Jun 20, 2018
#4
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so actually, the answer is 17

Jun 20, 2018