Question

Nine people decide to share some candy. The most anyone has is nine pieces, and one person does have nine pieces. At least one person ends up with no candy, by choice. The average (mean) number of pieces is four. Four is also the median. That means at least one person has four pieces. More people have two pieces of candy than any other number.

1 .Find all the possible solutions to the problem.

2 . List all possible solutions with representations- graphs, illustrations, etc

Answer 1

Sol:

  Write down the numbers 1 - 9 denoting the people with 1 getting the most number (9) and 9 getting the least which is 0 candy. You know that 4 is the median, which means the " middle person " gets 4 candy.

This is what you will get :

1 - 9 candy

2 - ?

3 - ?

4 - ?

5 - 4

6 - ?

7 - ?

8 - ?

9 - 0

The average is 4. Which gives the total number to be 9 * 4 = 36

You have the number of candy for 3 people, that total of the rest would be 36 - 9 - 4 - 0 = 23.

Most number of people get 2, so we go into different scenarios.

If the number of people with 2 candy is 2,

we can have:

1 - 9 candy

2 - 7

3 - 6

4 - 5

5 - 4

6 - 2

7 - 2

8 - 1

9 - 0

Remember that only 2 can repeat since more people have 2 pieces of candy that any other number.

From here, you just shift the numbers around or go on to the next scenario where the number of people with 2 candy is 3, and so on.