Pieces of Eight

Problem One

Students may like to solve the problem by writing the names of the people and fruit on pieces of card so that they can be moved into pairs. Students can then check each pairing to see whether they satisfy all the clues.
Another method, which is more useful for more difficult combination problems, is to use a table:

The crosses are made from the clue "No one likes fruit that starts with the same letter as their name.”
After the clue “Amy’s favourite fruit has no stone”, this becomes:

This leaves only one fruit for Pieta, the apple, and the peach is then left for Barbara.

Problem Two

Number sense and elimination are the most profitable strategies to use in this problem, with particular focus on the ones place of the answer.
For example:

Because only 7 + 9 = 16 puts a 6 in the ones place of the answer, this indicates that the tens places of the addends must be taken by 4 and 3.

As an extension, you can ask, “Are these the only possible answers you can get by arranging 4, 7, 3, and 9 as the addends?”
Three other answers are possible: 140, 113, 131.

Problem Three

Having a model of an octahedron available would be helpful for the students, but the problem can still be solved by visualisation. For example, students might see the edges as three groups of four.

Four edges meeting at the top vertex (corner)
Four edges around the middle
Four edges meeting at the bottom vertex (corner)

Answers to Problems

1. Amy likes bananas.
Barbara likes peaches.
Pieta likes apples.
2.

3. 6 corners, 12 edges