Puzzles · difficulty 1–5
Number problems that reward a method rather than a memorised formula: multi-step arithmetic, ratio and percentage sense, rates, and small tables where the trap is measuring against the wrong base. Every puzzle is solvable with mental arithmetic or a few written lines, so no calculator is needed.
25 puzzles · about 60 minutes end to end, as a guide only · untimed
The puzzles below run in difficulty order, easiest first. Each one checks on its own and shows its explanation straight away, so you get the method for one rung before you attempt the next.
Work the ladder from the top: the early puzzles need two clean steps, the last three need a named technique and an intermediate value carried exactly. Nothing here is timed and nothing is scored. Try the puzzle, take the hint if you stall, then read the explanation even when you were right — the method is the point, and the same wrong base or off-by-one turns up again and again.
A market stall opens with 84 punnets of berries. It sells 27 punnets before lunch and 35 punnets after lunch. How many punnets are left at the end of the day?
Subtract the two sales one after the other, then re-read exactly what the question asks you to report.
Two gardeners share 96 bulbs in the ratio 5 : 3, with the larger share going to the gardener who dug the beds. How many bulbs does the digger receive?
Count how many equal parts the ratio contains before you divide anything.
A cycling club has 240 members, and 35% of them ride at weekends only. How many members ride at weekends only?
Find 10% first, then scale that up to the percentage you actually need.
Over five shifts a volunteer sorted 8, 9, 15, 18 and 20 crates. What is the mean number of crates per shift?
Add all five values, then divide by how many values you added, not by how many gaps there are.
A roll of ribbon is 4.5 metres long. A craft group cuts it into pieces 25 centimetres long. How many whole pieces do they get?
Put both lengths into centimetres before you do anything else with them.
In a sale, a kettle is reduced by 20% and now costs £36. What was its price before the reduction?
The price you are given is not the whole; it is 80% of the number you are looking for.
A bottling machine fills 120 jars in 30 minutes at a steady rate. Working at the same rate, how many jars does it fill in 45 minutes?
Work out how many jars a single minute produces, then scale that up.
A fair spinner has eight equal sectors numbered 1 to 8. What is the probability that a single spin lands on a number greater than 5?
List the sectors that qualify rather than counting them in your head.
A tray holds red and blue counters in the ratio 3 : 4, and there are 18 red counters. Six more blue counters are added and no red ones. What is the new ratio of red to blue in its simplest form?
Convert the ratio into real counts of counters first, then add.
An L-shaped patio is a rectangle 8 metres by 5 metres with a rectangle 3 metres by 2 metres removed from one corner. What is the area of the patio?
Find the area of the complete rectangle first, then decide what the corner does to it.
The table shows loaves sold at three stalls on each day of one weekend. Across all three stalls, how many more loaves were sold on Sunday than on Saturday?
| Row | Saturday | Sunday |
|---|---|---|
| Rye stall | 46 | 58 |
| Seeded stall | 33 | 29 |
| Plain stall | 51 | 60 |
Total each day down its own column, and keep the sign of every stall's change.
Working alone, one painter takes 6 hours to paint a fence and another takes 12 hours. Working together, each at their own steady rate, how long do they take?
Ask how much of the fence each painter finishes in one hour, then combine those fractions.
A subscription price rises by 20% in spring, then falls by 20% in autumn. Compared with the price before the rise, what is the price after the fall?
Set the price at 100 and follow it through both changes, watching which figure each percentage is taken from.
A two-digit number has digits that add up to 11, and reversing its digits gives a number 27 greater than the original. What is the original number?
Reversing a two-digit number changes it by nine times the difference between its digits.
A festival stall opens every single day. Today is a Tuesday. What day of the week will it be exactly 100 days from today?
Divide by 7 and use nothing but the remainder.
A tutor marks two classes. The 12 learners in the morning class average 60 marks, and the 18 learners in the afternoon class average 70 marks. What is the mean mark across all 30 learners?
The classes are different sizes, so the two means cannot simply be averaged.
At a pottery stall, three mugs and two bowls cost £31 altogether, while one mug and two bowls cost £21 altogether. What does one mug cost?
Both purchases contain exactly the same number of bowls; use that to make the bowls disappear.
A bag holds 5 green beads and 3 yellow beads. Two beads are drawn out one after the other without replacement. What is the probability that at least one of them is yellow?
It is far quicker to work out the chance of drawing no yellow at all, then take that away from 1.
Five different books are placed in a row on a shelf. Two of them are cookery books and must stand next to each other. How many different arrangements of the five books are possible?
Treat the two cookery books as a single item, then remember they can still swap places inside it.
A courier rides 30 km at 15 km/h, stops for 20 minutes, then rides a further 12 km at 8 km/h. How long does the whole journey take, including the stop?
Time each leg separately with distance divided by speed, converting the decimal part of an hour with care.
Algae on a pond cover 8 square metres today and the covered area grows by 50% every week. What area do they cover three weeks from today?
Multiply by 1.5 once for each week rather than adding the same amount each time.
The table shows one hiring round. Which department made offers to the largest proportion of the people who applied to that department?
| Row | Applications | Offers made |
|---|---|---|
| Design | 60 | 15 |
| Support | 80 | 24 |
| Logistics | 200 | 40 |
| Finance | 150 | 27 |
Each department has to be judged against its own application total, not against the whole hiring round.
What is the smallest whole number greater than 1 that leaves a remainder of 1 when it is divided by 4, when it is divided by 5, and when it is divided by 6?
Take the remainder off first and look for the smallest number all three divisors go into exactly.
A club spends exactly £61 on badges costing £3 each and pens costing £7 each, buying at least one of each. It buys more pens than badges. How many pens does it buy?
List every whole number of the dearer item that fits inside the budget, then test each case against the remaining condition.
A tank holds 180 litres of water. On day one a third of the water is drawn off. On day two a quarter of what is then left is drawn off. On day three 25 litres are added. How much water is in the tank at the end of day three?
Each fraction applies to what is left at that stage, not to the amount you started with.
Each category maps onto the shared aptitude constructs, so a puzzle that interests you has a lesson and a larger practice bank behind it:
Arithmetic, fractions, percentages, ratios, rates, estimation, word problems, and number relationships.
Tables, charts, graphs, dashboards, trends, comparisons, and evidence-based conclusions.
Selecting methods, combining information, troubleshooting, and reaching practical solutions.
Sustained focus, selective attention, and accuracy under time pressure.
Evaluating evidence, assumptions, arguments, credibility, and alternative explanations.
Inferring rules from shapes, symbols, matrices, and non-verbal patterns.
Conditional logic, syllogisms, ordering, grouping, argument structure, and constraint problems.
