Family Mathematics Problem Solving
Sponsored by
The Somerville Mathematics Fund

The Family Mathematics problems are written for adults and children to work on together. They are not meant as another homework to be turned in to your child’s teacher, instead it is an opportunity for you to work together to solve a mathematical problem.
This Month’s Family Mathematics Problems are games for you to play and analyze. People play games all the time, not all games are fair, here are two games for you to decide whether they are fair or not. We hope you will enjoy playing together. Solution link is below.
The Somerville Mathematics Fund was founded in 2000 to celebrate and encourage mathematics achievement in the city of Somerville. We offer scholarships to students and grants to teachers.
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From March 2002
 Solutions
  


Family Mathematics Problem Solving: Grades 4, 5, 6

It’s a different game of “War”
There are an equal number of odd numbered and even numbered cards. When turning over the cards, there are four possibilities:
A turns over odd, B turns over odd, the product is odd, B gets the cards
A turns over even, B turns over odd, the product is even, A gets the cards
A turns over odd, B turns over even, the product is even, A gets the cards
A turns over even, B turns over even, the product is even, A gets the cards.
Theoretically, A gets the points 3 out of 4 times. This is not a fair game because A is going to win more often than B. You could make it a fair game by find the sum of the two cards.

 

 
Family Mathematics Problem Solving: Grades 7 and 8

One, Two, Three Show!
If you list all of the possible ways that the players can show the fingers, you should find that there are 27 different combinations. Player A gets a point if no one shows the same number of figers. This can be done six ways (123, 132, 213, 231, 312, 321). Player B gets a point if two people show the same number of fingers. This can be done 18 ways (112, 121, 211, 113, 131, 311, 221, 212, 122, 331, 313, 133, 233, 323, 332, 322, 232, 322). Player C gets a point if all three people show the same number of fingers. This can be done 3 ways (111, 222, 333). Theoretically, A should win 6/27 rounds, B should win 18/27 rounds and C should win 3/27 rounds. This is not a fair game.