Prime Number and Ans
Mathematical Puzzles
These puzzles (most of them old classics) from various sources can be used with pupils who finish classwork early. Most of the questions were chosen with enthusiastic, bright early teenagers in mind.
Some of the puzzles are also appropriate for class work - an initial worked example on the board will help a lot.
There are a few trick questions. Some questions can be quickly answered if you chance upon the right approach, but the 'long' solution isn't too arduous. Several of the questions are best answered by writing a computer program. Some are shown here. 1. How can you measure out exactly 4 litres of water from a tap using a 3 litre and a 5 litre bucket? Ans 2. 3litre 5litre 3. ----- ------ 4. 0 5 5. 3 2 6. 0 2 7. 2 0 8. 2 5 9. 3 4 10. A 24 litre bucket is full of lemonade. 3 men want to have equal amounts of it to take home, but they only have a 13 litre, a 5 litre and an 11 litre bucket. How do they do it? Ans 11. 24 13 11 5 12. ---------- 13. 24 0 0 0 14. 11 13 0 0 15. 6 13 0 5 16. 6 2 11 5 17. 8 0 11 5 18. 8 5 11 0 19. 8 13 3 0 20. 8 8 3 5 21. 8 8 8 0 22. A Queen (78kg), the Prince (36kg) and the King (42kg) are stuck at the top of a tower. A pulley is fixed to the top of the tower. Over the pulley is a rope with a basket on each end. One basket has a 30kg stone in it. The baskets are enough for 2 people or 1 person and the stone. For safety's sake there can't be more than a 6kg difference between the weights of the baskets if someone's inside. How do the people all escape? Ans 23. Basket 1 Basket 2 24. --------------------- 25. Stone up Prince down 26. King down Prince up 27. nothing up Stone down 28. Queen down Stone and King up 29. nothing up Stone down 30. Prince down Stone up 31. nothing up Stone down 32. King down Prince up 33. Stone up
These puzzles (most of them old classics) from various sources can be used with pupils who finish classwork early. Most of the questions were chosen with enthusiastic, bright early teenagers in mind.
Some of the puzzles are also appropriate for class work - an initial worked example on the board will help a lot.
There are a few trick questions. Some questions can be quickly answered if you chance upon the right approach, but the 'long' solution isn't too arduous. Several of the questions are best answered by writing a computer program. Some are shown here. 1. How can you measure out exactly 4 litres of water from a tap using a 3 litre and a 5 litre bucket? Ans 2. 3litre 5litre 3. ----- ------ 4. 0 5 5. 3 2 6. 0 2 7. 2 0 8. 2 5 9. 3 4 10. A 24 litre bucket is full of lemonade. 3 men want to have equal amounts of it to take home, but they only have a 13 litre, a 5 litre and an 11 litre bucket. How do they do it? Ans 11. 24 13 11 5 12. ---------- 13. 24 0 0 0 14. 11 13 0 0 15. 6 13 0 5 16. 6 2 11 5 17. 8 0 11 5 18. 8 5 11 0 19. 8 13 3 0 20. 8 8 3 5 21. 8 8 8 0 22. A Queen (78kg), the Prince (36kg) and the King (42kg) are stuck at the top of a tower. A pulley is fixed to the top of the tower. Over the pulley is a rope with a basket on each end. One basket has a 30kg stone in it. The baskets are enough for 2 people or 1 person and the stone. For safety's sake there can't be more than a 6kg difference between the weights of the baskets if someone's inside. How do the people all escape? Ans 23. Basket 1 Basket 2 24. --------------------- 25. Stone up Prince down 26. King down Prince up 27. nothing up Stone down 28. Queen down Stone and King up 29. nothing up Stone down 30. Prince down Stone up 31. nothing up Stone down 32. King down Prince up 33. Stone up