Question 980945
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.



<table border=1>
<tr><th>n</th><th>Number of unique ways</th><th>Sums</th></tr>
<tr><td>n=1</td><td>1</td><td>7</td></tr>
<tr><td>n=2</td><td>3</td><td>6+1,<font color="red">5+2</font>,4+3</td></tr>
<tr><td>n=3</td><td>4</td><td>5+1+1,<font color="red">4+2+1</font>,3+3+1,<font color="red">3+2+2</font></td></tr>
<tr><td>n=4</td><td>3</td><td>4+1+1+1,<font color="red">3+2+1+1</font>,2+2+2+1</td></tr>
<tr><td>n=5</td><td>2</td><td>3+1+1+1+1,<font color="red">2+2+1+1+1</font></td></tr>
<tr><td>n=6</td><td>1</td><td>2+1+1+1+1+1</td></tr>
<tr><td>n=7</td><td>1</td><td>1+1+1+1+1+1+1</td></tr>
</table>

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.