Logic is the hygiene the mathematician practices to keep his ideas healthy and strong.
-Herman Weyl
Problem 1
Rana, Toni, and Millie are sisters. Their ages are 9, 12, and 14 years. You need to deduce which sister is 9 years old, which one is 12 and which one is 14.
Clues:
Toni's age is not in the 4-times table.
Millie's age can be divided exactly by the number of days in a week.
Therefore, we can see that Toni is 9 years old, Rana is 12 years old and Millie is 14 years old.
Problem 2
Three students Bryan, Sean and Tony are discussing their favourite super heroes. You want to figure out who everyone’s favorite superheroes are and you want to know what age everyone is. Unfortunately you only managed to hear a few details from the conversation.
Bryan likes Spiderman.
Tony doesn’t like Superman.
The youngest student likes Spiderman.
The student who likes Superman is 8.
Everyone is a different age and likes a different hero.
The students’ ages are 6, 8 and 10 in some order.
Can you determine everyone’s age and favorite hero?
With the filled grid, you can see that you have the answer to your original question.
Bryan is 6 and he likes Spiderman.
Sean is 8 and he likes Superman.
Tony is 10 and she likes Batman.
Problem 3
Bill, John, Fred and Jim are married to one of Mrs Brown, Mrs Green, Mrs. Black and Mrs. White.
Clues:
Mrs. Brown's husband's name does not begin with J.
Mrs. Black's husband's name has the same letter twice.
Mrs. White's husband has three letters. Since Jim has only three letters on his name.
Therefore,
Fred is married to Mrs. Brown.
John to Mrs. Green
Bill to Mrs. Black
Jim to Mrs. White
Problem 4
Three girls; Angela, Lisa and Susan, met each other on their first day at logic summercamp. For an ice breaker, the girls created a logic grid to help them learn about each other’sfavourite colour, and what kind of pet they have. The camp counsellor who knew all of the girls’ favourite colours and what pets they have decided to give them these 4 hints:
Lisa, whose favourite colour is not green, has a fish.
Susan’s favourite colour is red.
The girl who likes green also has a dog.
None of the girls have the same type of pet or have the same favourite colour.
What other details can the 3 girls logically deduce about one another?
Therefore,
• Angela has a dog and her favourite colour is green;
• Lisa has a fish and her favourite colour is blue; and
• Susan has a cat and her favourite colour is red
Problem 5
Amanda, Jack, Mike and Rachel each travelled to a different part of the world in a different year. You have been hired to make a scrapbook of their journeys, but you can’t quite remember who went where and in what year. From looking at all of the photos you were given to put into the scrapbook, you can tell that the following 6 details must be true:
Neither Amanda or Jack traveled in 2015.
Mike didn’t travel to Rio de Janeiro.
Rachel traveled in 2014.
Amanda visited London.
Neither Mike or Rachel traveled to Tokyo.
A man traveled in 2016.
Can you make sure you properly label their scrapbook?
Solution:
Therefore,
• Amanda traveled to London in the year 2013;
• Jack traveled to Tokyo in the year 2016;
• Mike traveled to Sydney in the year 2015; and
• Rachel traveled to Rio de Janeiro in the year 2014.
Sources:
Unit 1 Section 1 : Logic Puzzles. (n.d.). https://www.cimt.org.uk/projects/mepres/book7/bk7i1/bk7_1i1.htm
University of WaterLoo, 2017. Grade 6 Math Circles. Logic Puzzles, Brain Teasers and Math Games. Centre for Education in Waterloo, Mathematics and Computing. https://cemc.uwaterloo.ca/events/mathcircles/2017-18/Fall/Junior6_Oct10_Soln.pdf