Puzzles are an untimed educational and entertainment activity. They are not a clinical, diagnostic, standardized, or professionally recognized assessment. Solving puzzles here does not produce an IQ score and cannot be used for Mensa qualification, diagnosis, giftedness identification, educational placement, employment selection, disability applications, accommodations, legal matters, or medical decisions. Puzzle items are never used as unseen scored questions in any Novus Learn assessment.
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.
Choose one answer for each item. Keep the authored hints, answer key, and worked explanations separate until you are ready to check your work.
Start here and establish the method before moving up the ladder.
1. puz-maths-puzzles-01: Berries before and after lunch · Difficulty 1
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?
Answer:
2. puz-maths-puzzles-02: Bulbs shared five to three · Difficulty 1
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?
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3. puz-maths-puzzles-03: Weekend-only riders · Difficulty 1
A cycling club has 240 members, and 35% of them ride at weekends only. How many members ride at weekends only?
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4. puz-maths-puzzles-04: Five shifts of crates · Difficulty 1
Over five shifts a volunteer sorted 8, 9, 15, 18 and 20 crates. What is the mean number of crates per shift?
Answer:
5. puz-maths-puzzles-05: Ribbon cut into lengths · Difficulty 1
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?
Answer:
Continue in order; use the worked explanations from earlier rungs when needed.
6. puz-maths-puzzles-06: The kettle after the sale · Difficulty 2
In a sale, a kettle is reduced by 20% and now costs £36. What was its price before the reduction?
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7. puz-maths-puzzles-07: Jars in three quarters of an hour · Difficulty 2
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?
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8. puz-maths-puzzles-08: The eight-sector spinner · Difficulty 2
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?
Answer:
9. puz-maths-puzzles-09: Six more blue counters · Difficulty 2
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?
Answer:
10. puz-maths-puzzles-10: The L-shaped patio · Difficulty 2
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?
Answer:
11. puz-maths-puzzles-11: Two days of loaves · Difficulty 2
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 |
Answer:
Continue in order; use the worked explanations from earlier rungs when needed.
12. puz-maths-puzzles-12: Two painters, one fence · Difficulty 3
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?
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13. puz-maths-puzzles-13: Up in spring, down in autumn · Difficulty 3
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?
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14. puz-maths-puzzles-14: Two digits and a reversal · Difficulty 3
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?
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15. puz-maths-puzzles-15: A hundred days from Tuesday · Difficulty 3
A festival stall opens every single day. Today is a Tuesday. What day of the week will it be exactly 100 days from today?
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16. puz-maths-puzzles-16: Two classes, one mean · Difficulty 3
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?
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17. puz-maths-puzzles-17: Mugs and bowls · Difficulty 3
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?
Answer:
Continue in order; use the worked explanations from earlier rungs when needed.
18. puz-maths-puzzles-18: At least one yellow bead · Difficulty 4
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?
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19. puz-maths-puzzles-19: Cookery books side by side · Difficulty 4
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?
Answer:
20. puz-maths-puzzles-20: The interrupted ride · Difficulty 4
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?
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21. puz-maths-puzzles-21: Three weeks of algae · Difficulty 4
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?
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22. puz-maths-puzzles-22: Offers against applications · Difficulty 4
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 |
Answer:
Continue in order; use the worked explanations from earlier rungs when needed.
23. puz-maths-puzzles-23: The same remainder three times · Difficulty 5
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?
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24. puz-maths-puzzles-24: Badges, pens and sixty-one pounds · Difficulty 5
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?
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25. puz-maths-puzzles-25: The tank over three days · Difficulty 5
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?
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