Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
35 questions · official format, shuffled order
1 The sum of the largest and the smallest of the numbers 3.5, 0.35, 35 and 0.035 is
Show worked solution
35 + 0.035 = 35.035.
2 Ana walks for 40 minutes at a steady speed. Ben walks for 20 minutes at twice Ana's speed. Ben walks
Show worked solution
Twice the speed for half the time covers the same distance as Ana.
3 How many even numbers less than 60 are multiples of 7?
Show worked solution
14, 28, 42, 56: 4.
4 Five square cards, each with a perimeter of 4 cm, are laid flat so that every card touches at least one other along a whole edge. What is the longest perimeter the pattern can have?
Show worked solution
Five cards in a row share only four edges: perimeter 2 × (5 + 1) = 12 cm. Any other arrangement shares more edges.
5 A rectangle is 20 cm long and 5 cm wide. How long is the side of a square with the same area?
Show worked solution
20 × 5 = 100 = 10 × 10, so 10 cm.
6 In a class every student plays tennis or chess or both. 17 play tennis, 12 play chess and 5 play both. How many students are in the class?
Show worked solution
17 + 12 − 5 = 24.
7 A piece of string is folded in half, then folded in half again. One cut is made straight through the middle of the folded string. How many pieces are there?
Show worked solution
A cut through 4 layers makes 4 cuts along the string, giving 5 pieces.
8 Figure 1 has 2 dots, figure 2 has 6, figure 3 has 12 and figure 4 has 20. How many dots does figure 9 have?
Show worked solution
Figure n is n by (n + 1). Figure 9 is 9 × 10 = 90.
9 What is the next number in this sequence?
Show worked solution
The gaps grow by one each time, so the next gap is 6: 16 + 6 = 22.
10 Between 12 noon and midnight, how many times do the two hands of a clock point in exactly opposite directions?
Show worked solution
The hands are opposite once every 65 minutes or so, which fits 11 times in 12 hours (6:00 is the one that falls on the hour, so the 5–6 and 6–7 hours share it).
11 Using only 5-cent, 10-cent and 20-cent coins, what is the fewest coins needed to make exactly 85 cents?
Show worked solution
Four 20s make 80, plus one 5: 5 coins. Three 20s leave 25, which needs two more coins, making 5 again — never 4.
12 Three apples and one pear weigh 500 g. One apple and three pears weigh 700 g. How much do one apple and one pear weigh together?
Show worked solution
4 apples + 4 pears = 1 200 g, so one of each is 1 200 ÷ 4 = 300 g.
13 A number is doubled and 7 is added. The result is 3 less than four times the number. What is the number?
Show worked solution
For 5: 2 × 5 + 7 = 17 and 4 × 5 − 3 = 17. ✓
14 How many squares of all sizes can be found in this 5 by 5 grid?
Show worked solution
25 + 16 + 9 + 4 + 1 = 55.
15 Lily is twice as old as Max. In 6 years she will be one and a half times as old as Max. How old is Max now?
Show worked solution
Max 6, Lily 12. In 6 years: 12 and 18, and 18 = 1.5 × 12 ✓.
16 A bell rings every 45 minutes, starting at 9:00 am. How many times does it ring from 9:00 am up to and including 3:00 pm?
Show worked solution
360 ÷ 45 = 8 gaps, so 9 rings (the one at 9:00 and one at the end of each gap).
17 Which of these is the largest?
Show worked solution
2 × 2 × 2 × 2 × 2 = 32, which beats 25, 27 and 30.
18 A cube is painted on all six faces and then cut into 27 equal small cubes. What fraction of the small cubes have no paint on them at all?
Show worked solution
Just the one cube in the very centre: 1/27.
19 A snail climbs 3 m up a 10 m pole each day and slips back 2 m each night. On which day does it reach the top?
Show worked solution
After 7 days and nights it is at 7 m. On the 8th day it climbs 3 m to 10 m and is at the top.
20 The average of four numbers is 15. One number is removed, and the average of the remaining three is 12. Which number was removed?
Show worked solution
4 × 15 = 60 and 3 × 12 = 36. 60 − 36 = 24.
21 Half of a number is 8 more than a quarter of the same number. What is the number?
Show worked solution
A quarter of the number is 8, so the number is 32.
22 A square is cut into two identical rectangles. Each rectangle has a perimeter of 30 cm. What is the perimeter of the original square?
Show worked solution
A rectangle's perimeter is 3s = 30, so s = 10 and the square's perimeter is 40 cm.
23 In a race, Ali finished before Bo but after Cy. Dee finished after Bo. Who came third?
Show worked solution
The order is Cy, Ali, Bo, Dee. Third is Bo.
24 A tank is two thirds full. After 15 litres are taken out it is exactly half full. How much does the tank hold?
Show worked solution
⅔ − ½ = ⅙ = 15 L, so the tank holds 6 × 15 = 90 L.
25 How many diagonals can be drawn inside a hexagon?
Show worked solution
6 corners × 3 diagonals each = 18, and each one was counted twice: 9.
26 A train 120 m long takes 6 seconds to pass a signal post completely. What is its speed in metres per second?
Show worked solution
120 ÷ 6 = 20 m/s.
27 If 3 cats catch 3 mice in 3 minutes, how many cats are needed to catch 10 mice in 10 minutes?
Show worked solution
Each cat catches 1 mouse every 3 minutes, so in 10 minutes 3 cats catch 10 mice: 3.
28 The digits 1 to 9 are each used exactly once to make three 3-digit numbers. What is the smallest possible total of the three numbers?
Show worked solution
Hundreds 1, 2, 3 → 600; tens 4, 5, 6 → 150; ones 7, 8, 9 → 24. Total 774 (for example 147 + 258 + 369).
29 Of 30 children, 18 like apples, 15 like bananas and 4 like neither. How many like both?
Show worked solution
18 + 15 − 26 = 7.
30 This net folds into a cube. Which face is opposite face 2?
Show worked solution
Faces 2 and 3 are the left and right arms, which become opposite faces. (4 is opposite 5, and 1 is opposite 6.)
31 A rope is cut into pieces 1.5 m long. This makes 8 pieces, with 0.7 m left over. How long was the rope?
Show worked solution
12 + 0.7 = 12.7 m.
32 What is the last digit of 7 × 7 × 7 × 7 × 7 × 7?
Show worked solution
The last digits go 7, 9, 3, 1, 7, 9 — the sixth is 9.
33 A rectangle's length is doubled and its width is halved. Its area is
Show worked solution
Doubling one side and halving the other cancels out: the area is the same.
34 Six people each shake hands once with every other person. How many handshakes are there?
Show worked solution
6 × 5 = 30, halved: 15.
35 A jar holds red and blue marbles in the ratio 3 : 5. When 10 more red marbles are added, the ratio becomes 1 : 1. How many blue marbles are there?
Show worked solution
2 parts = 10, so a part is 5 and blue is 5 × 5 = 25.