Australian AMC 2023 - Junior

Kurt paved his courtyard in the pattern shown. How many $1\times1$ pavers are in his courtyard?

Which of the following expressions has the smallest value?

The numbers on the top corners of these five playing cards add to 21. What is the number on the hidden card?

What is the value of $x$ in this diagram?

These two clocks show opening and closing times of my local Marine Discovery Centre. For how long is it open each day?

What is the value of $\dfrac{2+3+4}{7+8+9}$?

How many $25\text{ cm}\times25\text{ cm}$ squares fit in a $50\text{ cm}\times1\text{ m}$ rectangle?

This graph shows the water stored in my rainwater tank last May. What was the increase in water in the tank between the 10th and the 30th of May?

The sum of the ages of Ali, Bey and Cam is 32 years. What will be the sum of their ages in 3 years time?

A parallelogram $PQRS$ has an area of $60\text{ cm}^2$ and side $PQ$ of length $10\text{ cm}$. Which length is $6\text{ cm}$?

Mei can travel to her grandma’s house by a direct route, or by a scenic route that is 5 km longer. When she travels by the scenic route, and comes directly home, the round trip is 35 km. How long is the direct route?

In Nurdle, players guess a three-digit number. A tick ✓ means the digit is correct and in the right place; a circle ⊙ means the digit is in the number but in a different place; a cross × means the digit is not in the number at all. Mike’s two guesses and feedback are shown. How many different three-digit numbers fit all the clues?

| Guess | First position | Second position | Third position |
|---|---|---|---|
| 535 | 5: × | 3: ⊙ | 5: × |
| 123 | 1: × | 2: ✓ | 3: ⊙ |

In this triangle, the number in the centre of each side is the sum of the two numbers at the ends of that side. What is the sum of the three corner numbers?

A fuel tank is 40% empty. Then 40 litres of fuel is removed. The tank is now 40% full. How many litres are in a full tank?

The game Tutu uses 4 standard dice with opposite faces adding to 7. The dice are rolled and randomly arranged into a $2\times2$ block. A block’s score is the sum of the 4 numbers showing on top plus the sum of the 8 numbers showing around the outside. What is the largest possible score for the block shown?

The five clocks below are all showing the wrong time. One clock is 3 minutes away from the correct time and another is 7 minutes away. Which clock is closest to the correct time?

I wrote a list of all multiples of 7 between 1 and 500. Then I looked at the last digit of each number in my list. Which digit appeared most often as the last digit?

Amy designed this rectangular flag for her fleet of yachts. What fraction of the flag is shaded?

To unlock a security door, Daniyal enters a code on the keypad shown. The code has 10 digits, uses every digit exactly once, and moves between two buttons only when they touch. The code is as large as possible. What is its fifth digit?

Jake had 3 times as many gold balloons as blue balloons, and no other colours. Some blew away, leaving him with 5 times as many blue balloons as gold balloons. What is the smallest number of balloons he could have started with?