Logic Puzzles
Logic, from the Greek language, "the word" or "what is spoken" (coming to mean "thought" or "reason"), is systematic reasoning with clear support for a chain of statements that reaches a conclusion.
Logic puzzles require a mixture of academic skills; students must be able to read with an eye for meaningful detail as well as form a solution from several different possible combinations by considering combinations based on the evidence and confirming or rejecting them.
A logic puzzle usually begins with a description of an event wherein a variety of people with a variety of names have done a variety of things. Fragmented descriptions of the event in a series of statements reveal some details. Using the clues provided, you have to piece together what actually happened. This involves clear and logical thinking with support for each step using evidence from the text clues.
Two mathematical strategies that come in handy when tackling logic puzzles include making a drawing or diagram and making a table or chart. The type of diagram, sketch, table, or chart will vary based on the type of information given and each student's way of approaching and organizing new information.
Time and Talent (from Math Bafflers, Marilyn L. Rapp Buxton, 2011)
Three siblings are all musically and physically talented. Each child has a private music lesson and a private sports lesson each day. Music lessons are offered at 3:30, 4:00, and 5:30 pm at the conservatory, while sports lessons are offered at the field house at 4:30, 5:00, and 6:00 pm. Betty's saxophone lesson is 60 minutes earlier than Nadine's tennis lesson, but Betty's swimming lesson is 30 minutes later than Nadine's trumpet lesson. Also, Everett's guitar lesson is earlier than Nadine's tennis lesson, and Everett's golf lesson is 60 minutes earlier than Nadine's music lesson. Can you help get the children to their practices in time by identifying the children, lessons, and times correctly?
Identify the problem: Understand what we're being asked to do.
We need to identify the child, their music lesson time, and their sports lesson time.
Take Note of Patterns: Classify the different types of information given.
3 children with first names: Betty, Nadine, and Everett.
3 different sports: tennis, swimming, and racquetball.
3 different musical instruments: saxophone, trumpet, and tuba.
3 different music lesson times: 3:30, 4:00, and 5:30 pm.
3 different sports lesson times 4:30, 5:00, and 6:00 pm.
In this problem, the students are already clearly linked to their sport and their musical instrument, only the time is unclear.
Make a drawing, diagram, table, or chart representing what we know.
We need to identify the child, their music lesson time, and their sports lesson time. There are different ways to do this that will appeal to different students--
Three siblings are all musically and physically talented. Each child has a private music lesson and a private sports lesson each day. Music lessons are offered at 3:30, 4:00, and 5:30 pm at the conservatory, while sports lessons are offered at the field house at 4:30, 5:00, and 6:00 pm.
Betty's saxophone lesson is 60 minutes earlier than Nadine's tennis lesson, but Betty's swimming lesson is 30 minutes later than Nadine's trumpet lesson. Also, Everett's guitar lesson is earlier than Nadine's tennis lesson, and Everett's golf lesson is 60 minutes earlier than Nadine's music lesson.
Can you help get the children to their practices in time by identifying the children, lessons, and times correctly?
Betty's saxophone lesson is 60 minutes earlier than Nadine's tennis lesson, but Betty's swimming lesson is 30 minutes later than Nadine's trumpet lesson. Also, Everett's guitar lesson is earlier than Nadine's tennis lesson, and Everett's golf lesson is 60 minutes earlier than Nadine's music lesson.
Can you help get the children to their practices in time by identifying the children, lessons, and times correctly?
Scratch.mit.edu example of timeline and sketch
Break the paragraph into individual clues, and begin identifying certainties and eliminating possibilities.
- Betty's saxophone lesson is 60 minutes earlier than Nadine's tennis lesson.
- Betty's swimming lesson is 30 minutes later than Nadine's trumpet lesson.
- Everett's guitar lesson is earlier than Nadine's tennis lesson.
- Everett's golf lesson is 60 minutes earlier than Nadine's music lesson.
Represent your logical reasoning by--
circling solutions, and
crossing out impossibilities.
1. Betty's saxophone lesson is 60 minutes earlier than Nadine's tennis lesson.
Betty cannot have Music at 5:30, nor can Nadine have Sports at 6:00. Reasons--If Betty's music lesson were at 5:30, then Nadine's sport lesson would be at 6:30, and that is not a possibility in this puzzle. Nadine cannot have sports at 6:00, because then Betty would have to have music at 5:00, which is also not an option. A 3:30-to-4:30 match or a 4:00-to-5:00 match are still options, though.
2. Betty's swimming lesson is 30 minutes later than Nadine's trumpet lesson.
Betty cannot have Sports at 5:00, nor can Nadine have Music at 3:30. Reasons--If Nadine's music lesson were at 3:30, then Betty's sport lesson would be at 4:00, and that is not a possibility in this puzzle. Betty cannot have sports at 5:00, because then Nadine would have to have music at 4:30, which is also not an option.
3. Everett's guitar lesson is earlier than Nadine's tennis lesson.
Nadine now has a 4:30 or 5:00 sport, so Everett's music lesson is earlier than 5:00. He cannot have the 5:30 music lesson. Nadine's music lesson must be at 5:30, because she is the only one who can attend at that time. Betty's sport must be at 6:00, because it is 30 minutes that Nadine's music lesson (according to clue #2). Therefore, Everett cannot have the 6:00 sports lesson; he must be at 4:30 or 5:00.
4. Everett's golf lesson is 60 minutes earlier than Nadine's music lesson.
Nadine's music lesson at 5:30 means Everett's sport lesson must be at 4:30. He cannot go to sports again at 5:00, so Nadine is the only one able to attend a sports lesson at 5:00. Betty's music lesson must be at 4:00, because in clue #1 we learned her music is scheduled 60 minutes earlier than Nadine's sport lesson. By eliminating Betty's 3:30 music time and filling the 4:00 music time, Everett must have the 3:30 music lesson.