Ben scored 19 points in his last summer league basketball game.

In how many different ways could Ben have scored 19 points?   List them.

Note: in basketball, you can score points in three different ways:
a three-pointer, a two point field goal, or a free throw (1 point).



Solution to the Problem:


There are 40 ways that Ben could have scored 19 points.

Here are the possibilities:
  3 Ptr     2 Ptr     free throw  
  6     0     1  
  5     2     0  
  5     1     2  
  5     0     4  
  4     3     1  
  4     2     3  
  4     1     5  
  4     0     7  
  3     5     0  
  3     4     2  
  3     3     4  
  3     2     6  
  3     1     8  
  3     0     10  
  2     6     1  
  2     5     3  
  2     4     5  
  2     3     7  
  2     2     9  
  2     1     11  
  2     0     13  
  1     8     0  
  1     7     2  
  1     6     4  
  1     5     6  
  1     4     8  
  1     3     10  
  1     2     12  
  1     1     14  
  1     0     16  
  0     9     1  
  0    8     3  
  0    7     5  
  0     6     7  
  0     5     9  
  0     4     11  
  0     3     13  
  0     2     15  
  0     1     17  
  0     0     19  


Here is Ritwik Chaudhuri's analysis of the problem:




Correctly solved by:

1. Colin (Yowie) Bowey Beechworth, Victoria, Australia
2. K. Sengupta Calcutta, India
3. Ritwik Chaudhuri Santiniketan, West Bengal, India
4. Ivy Joseph Pune, Maharashtra, India
5. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
6. Luis Banuelas Central High School,
Grand Junction, Colorado
8. Paul Muckleshoot Tribal School,
Auburn, Washington
9. Austin Hale Central High School,
Grand Junction, Colorado
10. Finn Kohser Downingtown Stem Academy,
Downingtown, Pennsylvania
11. Kelly Stubblefield Mobile, Alabama