Dining Ducks
3 out of 3
Use the information about the ducks on a particular farm to find out which of the statements about them must be true.
Problem
Every healthy duck is greedy and every old duck is greedy.
On a particular farm, some ducks are greedy and some ducks are not.
Which of the following statements about the ducks on that farm must be true?
- There are both young ducks and old ducks.
- All the ducks that are not greedy are young.
- Some of the young ducks are sick.
- All the sick ducks are young.
This problem has been adapted from the book "Sums for Smart Kids" by Laurie Buxton, published by BEAM Education, which is now out of print.
Getting Started
Try drawing a Venn diagram to show the information you are given.
Student Solutions
Denise sent in her solution.
1.There must be young ducks, but there don't have to be any old ducks. This is because if there were only old ducks, then they would all be greedy, and we know that there are some that aren't greedy.
2.This is true. We can't have a duck that is both not greedy and old, and there are ducks that are not greedy, so they must be young.
3. This is also true. If all of the young ducks were healthy, then they'd all be greedy. But all of the old ducks are also greedy, so then there wouldn't be any ducks that aren't greedy. So some of the young ducks are sick.
4. We don't know whether or not this is true. We could have old ducks that are sick.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
Possible approach