Question 980945: A partition of a positive integer n is any way of writing n as a sum of one or more positive integers, in which we don't care about the order of the numbers in the sum. For example, the number 4 can be written as a sum of one or more positive integers ( which we don't care about the order of the numbers in the sum ) in exactly five ways:
4, 3+1, 2+2, 2+1+1, 1+1+1+1
So 4 has five partitions.
What is the number of partitions of the number 7?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Adding up to 7
n = number of addends
Eg: n = 3 means we are adding 3 numbers to get to 7. The table shows 4 ways to add up 3 numbers to get to 7.
| n | Number of unique ways | Sums |
|---|
| n=1 | 1 | 7 |
| n=2 | 3 | 6+1,5+2,4+3 |
| n=3 | 4 | 5+1+1,4+2+1,3+3+1,3+2+2 |
| n=4 | 3 | 4+1+1+1,3+2+1+1,2+2+2+1 |
| n=5 | 2 | 3+1+1+1+1,2+2+1+1+1 |
| n=6 | 1 | 2+1+1+1+1+1 |
| n=7 | 1 | 1+1+1+1+1+1+1 |
Note: the sums in red aren't special. They are done in red to provide alternating colors (red and black) so the sums stand out a bit better.
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