Hints and solutions to
Make a List #1
Take 25 marbles. Put them in 3 piles so an odd number is in each pile. How
many ways can this be done?
Take 25 marbles. Put them in 3 piles so an odd number is in each pile. How
many ways can this be done?
- This week the solution strategy is to make a systematic list of all the possibilities (or at least enough so that a pattern can be discerned). Today's problem is a good example:
- The organizing principle is to have the (odd) number in the first pile increase from 1 the slowest, the second pile the next slowest, and the third pile's number will decrease so that the sum is 25.
- We can make the table shorter if we assume we're looking for all the different ways to do this -- so we assume that 3+7+15 is the same as 15+3+7. To keep all the groupings different, we'll always assume the first pile is the smallest, the second next smallest and the third pile is the biggest (although ties are allowed).
- Here is the table:
Pile 1
Pile 2
Pile 3
1
1
23
1
3
21
1
5
19
1
7
17
1
9
15
1
11
13
3
3
19
3
5
17
3
7
15
3
9
13
3
11
11
5
5
15
5
7
13
5
9
11
7
7
11
7
9
9
That's it - so there are only 16 different ways to do this.