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Logic Problems

Help Tina, Josh, Dawn, and Mark find their nicknames - Spider, Curly, Ace, Fudgy - using given clues and logic steps.

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Logic Problems

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  1. Logic Problems Lesson 1

  2. Learning Objectives: • To use one piece of information to see what effect it has. • To use a recording system to organise the given information. • To check that the answer meets the given criteria.

  3. Meet my four volunteers: Tina Josh Dawn Mark

  4. Nicknames • Dawn, Mark, Josh and Tina are friends. • They each have a nickname. • Their nicknames are Spider, Curly, Ace and Fudgy, but not in that order. • What is the nickname of each of the friends? • Clues • Josh plays tennis with Curly and goes swimming with Ace. • Tina has been on holiday with Curly but travels to school with Fudgy. • Spider, Curly and Dawn play in the football team. • Spider sometimes goes to tea with Josh.

  5. So, how do we start?

  6. So, how do we start? • First we need to think about what we can learn from the information we are given. • Each child could be called by each nickname, so let’s start there.

  7. We’ll start by writing all four nicknames underneath each child. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  8. We’ll can cross out each name as we decide it can’t be the correct one. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  9. We’ve been given a number of clues to help us work out which nickname belongs to each child.Here they are. Clues • Josh plays tennis with Curly and goes swimming with Ace. • Tina has been on holiday with Curly but travels to school with Fudgy. • Spider, Curly and Dawn play in the football team. • Spider sometimes goes to tea with Josh.

  10. With this type of problem it often makes sense to start with the first piece of information and work through them in order. However, that doesn’t always work. Don’t be surprised if you sometimes can’t learn anything from the first clue the first time you look! We now need to work carefully through the clues.

  11. The first clue tells us that Joshplays tennis with Curlyand goes swimming with Ace.

  12. The first clue tells us that Joshplays tennis with Curlyand goes swimming with Ace. • What does this tell us about Josh?

  13. The first clue tells us that Joshplays tennis with Curlyand goes swimming with Ace. • What does this tell us about Josh? • It tells us that Josh cannot be the same person as Curly or Ace, if he does activities with both of them • So Josh’s nickname cannot be Curly and it cannot be Ace.

  14. Let’s show that on our picture. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  15. We could now go straight on to the second clue, but I think something else makes more sense.Can you spot it?

  16. We could now go straight on to the second clue, but I think something else makes more sense.Can you spot it? • That’s right! There’s another clue about Josh. • Lets look at that one next.

  17. The fourth clue tells us that Spider sometimes goes to tea with Josh.What can we learn from that?

  18. The fourth clue tells us that Spider sometimes goes to tea with Josh.What can we learn from that? Spider cannot be Josh’s nickname either!

  19. If we add that to our picture, this is what we have. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  20. What do we now know must be true? Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  21. Josh’s nickname must be Fudgy!!

  22. Josh’s nickname must be Fudgy!! • What else do we therefore know?

  23. Josh’s nickname must be Fudgy!! • What else do we therefore know? • If Josh’s nickname is Fudgy, no one else can have that nickname.

  24. Josh’s nickname must be Fudgy!! • What else do we therefore know? • If Josh’s nickname is Fudgy, no one else can have that nickname. • Let’s add that to the diagram.

  25. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  26. Clue number 2 tells us that Tinahas been on holiday with Curlybut travels to school with Fudgy.

  27. Clue number 2 tells us that Tinahas been on holiday with Curlybut travels to school with Fudgy. • So we know that Tina’s nickname cannot be Curly or Fudgy.

  28. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  29. Does that help us learn anything for certain?

  30. Does that help us learn anything for certain?No, so we move on to another clue.

  31. There’s just one more clue we haven’t looked at. • The third clue tells us that Spider, Curly and Dawn play in the football team.

  32. There’s just one more clue we haven’t looked at. • The third clue tells us that Spider, Curly and Dawn play in the football team. • So that must mean that Dawn cannot be Spider or Curly.

  33. Dawn cannot be Spider or Curly. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  34. We already knew Dawn couldn’t be Fudgy so she must be Ace. And… ? Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  35. No one else can be Ace. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  36. At this point it’s always a good idea to look though the clues again to check you haven’t missed anything. Have we? We’ve looked at all the clues once.

  37. At this point it’s always a good idea to look though the clues again to check you haven’t missed anything. Have we? No, so all the information we need must now be on our picture. Can we learn anything else? We’ve looked at all the clues once.

  38. What can you see? Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  39. Tina must be Spider! Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  40. And? Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  41. Mark cannot be Spider, so he must be Curly. Tina Josh Dawn Mark Spider Spider Spider Spider Curly Curly Curly Curly Ace Ace Ace Ace Fudgy Fudgy Fudgy Fudgy

  42. Dawn ~ Ace Mark ~ Curly Josh ~ Fudgy Tina ~ Spider Our solution to the problem is:

  43. Dawn ~ Ace Mark ~ Curly Josh ~ Fudgy Tina ~ Spider Look back at the criteria and clues for the problem. Does this solution fit with the information we were given? Our solution to the problem is:

  44. Dawn ~ Ace Mark ~ Curly Josh ~ Fudgy Tina ~ Spider Look back at the criteria and clues for the problem. Does this solution fit with the information we were given? Yes it does so we are correct! Our solution to the problem is:

  45. Like with the car-parking problem, the pictures are great, but we’ve had to write the nicknames out four times. There must be a more efficient way. Any ideas?

  46. Like with the car-parking problem, the pictures are great, but we’ve had to write the nicknames out four times. There must be a more efficient way. Any ideas? This type of problem works very well set out as a table.

  47. Write each name down one side and each nickname along the top.

  48. As we work through the clues again, we can add ticks or crosses in the boxes, depending on what we have learnt.

  49. Josh cannot be Curly or Ace.

  50. Josh cannot be Spider sohe must be Fudgy.

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