document.write( "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:
\n" ); document.write( "4, 3+1, 2+2, 2+1+1, 1+1+1+1
\n" ); document.write( "So 4 has five partitions.
\n" ); document.write( "What is the number of partitions of the number 7? \n" ); document.write( "

Algebra.Com's Answer #602000 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Adding up to 7\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "n = number of addends
\n" ); document.write( "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.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\r\n" ); document.write( "\n" ); document.write( "

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

\r
\n" ); document.write( "\n" ); document.write( "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. \n" ); document.write( "

\n" );