Some octopuses, fish and a few mermaids are in a rock pool.

Altogether there are 38 arms, 24 eyes and 8 tails in the pool.

How many mermaids are there?

Find strategies for investigating number problems.

Students are likely to use logical deduction, guess and check, or make a table to solve this problem.

It is similar to the Level 2 problem, Pigs and Ducks.

### The Problem

Some octopuses, fish and a few mermaids are in a rock pool. Altogether there are 38 arms, 24 eyes and 8 tails in the pool.

How many mermaids are there?

### Teaching sequence

- Pose the problem and have students restate it in their own words. Ask:
*What are the key numbers?*

What is the key information?

How will you use the fact that there are octopuses? mermaids? fish? - As students work on the problem in groups or individually, ask:
*Tell me the information that you are using. Write it down in some way.**What information can you get from these facts?*

How are you keeping track of what you find out? - Make the Extension problem available.
- As groups report back have them explain and compare their strategies.

#### Extension to the problem

Write a problem like this one that has three different types of creatures and three body parts.

#### Solution

This is helpful information that can be deduced: Fish don’t have arms so the arms come from the octopuses and the mermaids. All of the creatures have two eyes and since there are 24 eyes there must be 12 creatures. Octopuses don’t have tails so there are 8 fish and mermaids.

Therefore, there are 12 creatures, 8 of which are fish and mermaids, and 12 – 8 = 4 octopuses.

4 octopuses contribute 4 x 8 = 32 arms. That leaves 38 – 32 = 6 arms for the mermaids. There must be 3 mermaids.

The problem can also solved using a diagram, a table, or by using guess and check. If a group uses guess and check and gets the right answer, you might like to suggest that they try to find another way.