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 Locker codes
A school locker code is three digits long. Each digit can be any of 0–9, and digits may be repeated.
How many different codes are possible?
A school locker code is three digits long. Each digit can be any of 0–9, and digits may be repeated.
How many different codes are possible?
Show worked solution
10 × 10 × 10 = 1000. Adding the slots would give 30, and 3000 comes from 10 × 10 × 10 × 3.
2 Locker codes
A school locker code is three digits long. Each digit can be any of 0–9, and digits may be repeated.
Someone knows their code uses the digits 2, 5 and 8 exactly once each, but not the order. How many codes could it be?
A school locker code is three digits long. Each digit can be any of 0–9, and digits may be repeated.
Someone knows their code uses the digits 2, 5 and 8 exactly once each, but not the order. How many codes could it be?
Show worked solution
3 × 2 × 1 = 6. (9 would be 3 × 3, which wrongly allows repeats.)
3 Balance
A balance holds weights hanging from two arms, and it is perfectly level. All weights of the same shape have the same mass, and every mass is a whole number of kilograms. The total mass of all the weights shown is 24 kg.
What is the mass of one hexagon weight?
A balance holds weights hanging from two arms, and it is perfectly level. All weights of the same shape have the same mass, and every mass is a whole number of kilograms. The total mass of all the weights shown is 24 kg.
What is the mass of one hexagon weight?
Show worked solution
Two hexagons balance one square, so the square is twice a hexagon. All the weights are 2 hexagons + 1 square = 4 hexagons = 24 kg, so one hexagon is 6 kg.
4 Balance
A balance holds weights hanging from two arms, and it is perfectly level. All weights of the same shape have the same mass, and every mass is a whole number of kilograms. The total mass of all the weights shown is 24 kg.
What is the mass of the square weight?
A balance holds weights hanging from two arms, and it is perfectly level. All weights of the same shape have the same mass, and every mass is a whole number of kilograms. The total mass of all the weights shown is 24 kg.
What is the mass of the square weight?
Show worked solution
A hexagon is 6 kg and the square balances two of them, so the square is 12 kg. Check: 6 + 6 + 12 = 24 kg. ✓
5 Market stalls
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
How many of the six products are available in May?
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
How many of the six products are available in May?
Show worked solution
In May, F2, V1 and B1 are available — 3 products. F1 stops in April, V2 starts in September and B2 starts in June.
6 Market stalls
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
A hamper must contain one fruit, one vegetable and one bread, all available in the same month. In how many months of the year is a hamper impossible?
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
A hamper must contain one fruit, one vegetable and one bread, all available in the same month. In how many months of the year is a hamper impossible?
Show worked solution
No vegetable is available in January or February, so a hamper is impossible in those 2 months. (January also has no bread.) It is possible in the other ten.
7 Market stalls
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
Which product is available in the greatest number of months?
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
Which product is available in the greatest number of months?
Show worked solution
F2 is available all 12 months. B1 is a close second at 11 months, V1 has 6 and F1 has 4.
8 Market stalls
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
How many of the six products are available in July?
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
How many of the six products are available in July?
Show worked solution
In July: F2, V1, B1 and B2 — 4 products. Be careful to use the July column, since June, July and January all begin with J.
9 Market stalls
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
In how many months can a hamper be made that contains V2 as its vegetable?
A market stall sells six products. F1 and F2 are fruit, V1 and V2 are vegetables, and B1 and B2 are bread. The grid shows the months in which each is available; a shaded square means available.
In how many months can a hamper be made that contains V2 as its vegetable?
Show worked solution
V2 runs September to December — 4 months. F2 is available all year and B1 covers February to December, so a hamper works in all 4 of them.
10 Tournament
Four teams play a tournament in which every team plays every other team once. A win scores 2 points, a draw 1 and a loss 0. The table shows the results after each team has played two games. The Ibis row is missing.
What are the Ibis results from their two games?
Four teams play a tournament in which every team plays every other team once. A win scores 2 points, a draw 1 and a loss 0. The table shows the results after each team has played two games. The Ibis row is missing.
What are the Ibis results from their two games?
Show worked solution
Each of the 4 teams has played twice, which is 4 games, and every game awards 2 points in total — so 8 points have been given out. Falcons 4 + Hawks 3 + Jays 0 = 7, leaving Ibis with 1 point: one draw and one loss.
11 Tournament
Four teams play a tournament in which every team plays every other team once. A win scores 2 points, a draw 1 and a loss 0. The table shows the results after each team has played two games. The Ibis row is missing.
Each team has one game still to play. Which teams could finish the tournament with the most points?
Four teams play a tournament in which every team plays every other team once. A win scores 2 points, a draw 1 and a loss 0. The table shows the results after each team has played two games. The Ibis row is missing.
Each team has one game still to play. Which teams could finish the tournament with the most points?
Show worked solution
Best finals: Falcons 6, Hawks 5, Ibis 3, Jays 2. The Falcons finish on at least 4, so Ibis and Jays can never catch them — but if the Falcons lose and the Hawks win, the Hawks finish on 5 against 4. So Falcons or Hawks.
12 Data transfer
Data is sent across a network in packets. If a packet fails to send, it is sent again immediately at half the previous rate, halving again on each further failure.
About how many packets can be sent per second at the initial rate?
Data is sent across a network in packets. If a packet fails to send, it is sent again immediately at half the previous rate, halving again on each further failure.
About how many packets can be sent per second at the initial rate?
Show worked solution
50 000 000 ÷ 5000 = 10 000 packets a second.
13 Data transfer
Data is sent across a network in packets. If a packet fails to send, it is sent again immediately at half the previous rate, halving again on each further failure.
One gigabit is 1000 million bits. How long would a 2-gigabit file take at the initial rate?
Data is sent across a network in packets. If a packet fails to send, it is sent again immediately at half the previous rate, halving again on each further failure.
One gigabit is 1000 million bits. How long would a 2-gigabit file take at the initial rate?
Show worked solution
2 gigabits is 2 000 000 000 bits, and 2 000 000 000 ÷ 50 000 000 = 40 seconds.
14 Data transfer
Data is sent across a network in packets. If a packet fails to send, it is sent again immediately at half the previous rate, halving again on each further failure.
Packet A sent on the first attempt. Packet B failed twice and sent on the third attempt. Compared with packet A, how long did packet B take in total?
Data is sent across a network in packets. If a packet fails to send, it is sent again immediately at half the previous rate, halving again on each further failure.
Packet A sent on the first attempt. Packet B failed twice and sent on the third attempt. Compared with packet A, how long did packet B take in total?
Show worked solution
Attempt 1 takes the same time as A. Attempt 2 runs at half the rate, so it takes twice as long, and attempt 3 takes four times as long. Altogether 1 + 2 + 4 = seven times as long.
15 Reef survey
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
A site records 60 fish in one survey. What is the best estimate of its coral cover?
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
A site records 60 fish in one survey. What is the best estimate of its coral cover?
Show worked solution
On the coral-against-fish graph, 60 fish corresponds to dots sitting around 50% coral cover.
16 Reef survey
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
A site is 15 metres deep. What is the best estimate of its coral cover?
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
A site is 15 metres deep. What is the best estimate of its coral cover?
Show worked solution
On the depth-against-coral graph, 15 m corresponds to about 60% coral cover.
17 Reef survey
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
Which statement is most consistent with the data?
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
Which statement is most consistent with the data?
Show worked solution
The first cloud slopes down, so deeper sites tend to have less coral cover. "All" is disproved by dots with coral at 30 m and beyond, "no effect" contradicts the slope, and a graph cannot show a cause.
18 Reef survey
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
A site is 15 metres deep. About how many fish would you expect it to record?
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
A site is 15 metres deep. About how many fish would you expect it to record?
Show worked solution
Coral cover is the bridge. 15 m gives about 60% coral on the first graph, and 60% coral gives about 70 fish on the second.
19 Reef survey
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
Which claim about coral cover and fish numbers is safest to make from these data?
Divers surveyed reef sites. At each site they recorded the water depth, the percentage of the seabed covered by coral, and the number of fish counted in one survey. Each dot is one site.
Which claim about coral cover and fish numbers is safest to make from these data?
Show worked solution
More coral cover is associated with more fish describes the upward cloud and claims nothing beyond it. "Causes" goes past what a graph can show, "every … exactly" is disproved by the scatter, and "unrelated" contradicts the slope.
20 Rainwater
A rectangular roof collects rainwater into a tank. Assume all the rain landing on the roof reaches the tank, and that 1 cubic metre is 1000 litres.
Roughly how many litres of rain land on the roof in a year?
A rectangular roof collects rainwater into a tank. Assume all the rain landing on the roof reaches the tank, and that 1 cubic metre is 1000 litres.
Roughly how many litres of rain land on the roof in a year?
Show worked solution
The roof is 12 × 10 = 120 square metres, and 600 mm is 0.6 m, so the volume is 120 × 0.6 = 72 cubic metres. At 1000 litres each that is 72 000 litres.
21 Marble jar
A jar holds 12 red, 12 blue and 12 green marbles, identical apart from colour. Marbles are taken out at random without looking.
What is the smallest number of marbles that must be taken to be sure of having a matching pair?
A jar holds 12 red, 12 blue and 12 green marbles, identical apart from colour. Marbles are taken out at random without looking.
What is the smallest number of marbles that must be taken to be sure of having a matching pair?
Show worked solution
Three marbles could be one of each colour, but there is no fourth colour, so the fourth must match one already held: 4.
22 Marble jar
A jar holds 12 red, 12 blue and 12 green marbles, identical apart from colour. Marbles are taken out at random without looking.
What is the smallest number that must be taken to be sure of having a green pair?
A jar holds 12 red, 12 blue and 12 green marbles, identical apart from colour. Marbles are taken out at random without looking.
What is the smallest number that must be taken to be sure of having a green pair?
Show worked solution
All 12 red and all 12 blue could come out first — 24 marbles with no green. Two more are then forced to be green, so 26.
23 Marble jar
A jar holds 12 red, 12 blue and 12 green marbles, identical apart from colour. Marbles are taken out at random without looking.
What is the smallest number that must be taken to be sure of having a pair of each colour?
A jar holds 12 red, 12 blue and 12 green marbles, identical apart from colour. Marbles are taken out at random without looking.
What is the smallest number that must be taken to be sure of having a pair of each colour?
Show worked solution
All 12 red then all 12 blue gives 24 marbles and two pairs, but no green. Two more must be green, so 26 — the same total as the last question, but reached by a different run.
24 Relay stations
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
A message starts at P. Which station is it at after two steps?
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
A message starts at P. Which station is it at after two steps?
Show worked solution
P transmits to X, and X relays to Q.
25 Relay stations
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
A message starts at Q. Which station is it at after three steps?
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
A message starts at Q. Which station is it at after three steps?
Show worked solution
Q → Y (transmit), Y → R (relay), R → Z (transmit).
26 Relay stations
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
A message starts at P. After how many steps does it first return to P?
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
A message starts at P. After how many steps does it first return to P?
Show worked solution
P → X → Q → Y → R → Z → P, which is 6 steps. The system is a single loop through all six stations.
27 Relay stations
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
Which station does a message reach from R in exactly one step?
Six relay stations are arranged in two groups. Each station on the left transmits to exactly one station on the right, shown by a solid line. Each station on the right then relays to one station on the left, shown by a dashed arrow. A message moves one step at a time along these links.
Which station does a message reach from R in exactly one step?
Show worked solution
R transmits to Z. It reaches P only after a second step, when Z relays back.
28 Shuttle loop
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
Which stop is the shuttle at at 09:00?
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
Which stop is the shuttle at at 09:00?
Show worked solution
An hour is six 10-minute steps, and the loop has six stops, so the shuttle is back at the Depot.
29 Shuttle loop
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
Which stop is the shuttle at at 10:20?
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
Which stop is the shuttle at at 10:20?
Show worked solution
10:20 is 140 minutes after 08:00, which is 14 steps. Two whole loops use 12, leaving 2 steps past the Depot: Mill, then Quay.
30 Shuttle loop
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
How many times does the shuttle reach Ridge between 08:00 and 12:00?
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
How many times does the shuttle reach Ridge between 08:00 and 12:00?
Show worked solution
Ridge is three steps after the Depot, so 08:30, and then every 60 minutes: 08:30, 09:30, 10:30 and 11:30 — 4 times before 12:00.
31 Shuttle loop
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
How long does the shuttle take to complete one full loop?
A shuttle bus runs a continuous loop of six stops, reaching a new stop every 10 minutes. It is at the Depot at 08:00 and travels Depot, Mill, Quay, Ridge, Sands, Tower, then Depot again.
How long does the shuttle take to complete one full loop?
Show worked solution
6 × 10 = 60 minutes.
32 Plant study
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
Which combination produced the greatest average height gain?
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
Which combination produced the greatest average height gain?
Show worked solution
The largest value is 14 cm, in the "lots" row and "high light" column: lots of water with high light.
33 Plant study
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
Consider the group grown with medium light and lots of water. What was the total height gain for that whole group?
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
Consider the group grown with medium light and lots of water. What was the total height gain for that whole group?
Show worked solution
That cell reads 12 cm per plant, and there were 8 plants in the group, so 12 × 8 = 96 cm. (12 cm forgets the group entirely.)
34 Plant study
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
The plants were grown for four weeks but measured only in the fourth week. The most likely reason is:
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
The plants were grown for four weeks but measured only in the fourth week. The most likely reason is:
Show worked solution
Measuring in week 1 would catch plants that had barely begun to respond to their light and water, so the readings would not reflect the conditions. Waiting gives them time — to give the plants time to respond to the conditions. Convenience is never the design reason.
35 Plant study
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
Increasing the light from low to high, at every watering amount, always increases:
Scientists grew plants under three light levels and three watering amounts, giving nine combinations. Each combination was given to a group of 8 plants. The plants were grown for four weeks, and the measurements were taken in the fourth week. The tables give the averages per plant.
Increasing the light from low to high, at every watering amount, always increases:
Show worked solution
Height gain rises across every row: 2→3→4, 6→9→11 and 7→12→14. Leaf number does not — the "none" row runs 4→5→5, and 5 is not more than 5. So height gain only.