Problem of the Week

Below is a selection of problems that are representative of the type of questions included in the APSMO papers. Please note that the solutions provided are not comprehensive and are intended to provide an overview only. If you would like more comprehensive examples of questions and solutions, please purchase one of our books or register for a program.

Find My Numbers
Suitable for Years 1 & 2 (mainstream)

I’ve chosen 3 of these numbers: 1,2,3,4,5,6,7,8. See if you can find them.
My numbers add up to 7.
One of my numbers is 4.
Which 3 numbers did I choose?

Suitable for Years 1 & 2 (mainstream)

My piggybank was empty but I have just put in 50c.
I only put in 10c coins or 20c coins.
What different combinations of coins might be inside?

Suitable for Years 3 & 4 (mainstream)

At the beach, Jonah collected 15 shells.
Hugo collected the same number of shells as Ava.
When they combined the shells and shared them evenly, each child got 11 shells.
How many shells did Ava collect?

Find My Numbers

I’ve chosen 3 of these numbers: 1,2,3,4,5,6,7,8. See if you can find them.
My numbers add up to 7.
One of my numbers is 4.
Which 3 numbers did I choose?

Coins

My piggybank was empty but I have just put in 50c.
I only put in 10c coins or 20c coins.
What different combinations of coins might be inside?

Shells

At the beach, Jonah collected 15 shells.
Hugo collected the same number of shells as Ava.
When they combined the shells and shared them evenly, each child got 11 shells.
How many shells did Ava collect?

Orange Slices

Your team has won the championship!
You are excited but exhausted.
There are slices of orange to share!
If the slices are shared equally between the players, everyone gets 4 slices.
However, if they are shared equally between the players, the coach and
the team manager, everyone gets 3 slices.
How many players are on the team?

Run Run Run

There are more than 20 solutions for this cryptarithm.
Can you find the SMALLEST possible solution?
Remember:
In a cryptarithm every letter must represent a different digit.

World Cup Fever!

There are 22 soccer players on the field.
7 players have taken a corner kick.
6 players have taken a throw in.
3 players have done both.
How many of the players have done neither?

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