October 2011 - Page 10 of 10 - Math and Multimedia

The Codebreaker Game

October 4, 2011 GB Games and Puzzles, Math Lite

Codebreaker is an online logic game that allows the player to guess a correct color combination “code.” In each guess (represented by the rows of circles in the leftmost part of the diagram), the computer places black circles in smaller pegs (see circles below the Accept button in the diagram) to indicate the number of colors in the right position, and white circles to indicate the number of correct colors in the wrong position. The player is allowed up to eight guesses to win the game, otherwise he loses.

The Codebreaker Game is very similar to Mastermind, a well-known board invented by Mordecai Meirowitz. It’s a good game for developing critical thinking of students. A good activity would be to let students develop their own strategy of making the least number of guesses in breaking the code.

Leave a comment logic games, master mind, math games, math puzzles, mordecai meirowitz

Milkshakes and Power Sets

October 3, 2011 GB College Mathematics, Combinatorics, Set Theory

In Milkshakes, Beads, and Pascal’s Triangles, we have talked about a systematic way of choosing a combination of objects from a larger number of objects. Let us recall the problem in the said post.

Issa went to a shake kiosk and want to buy a milkshake. The shake vendor told her that she can choose plain milk, or she can choose to combine any number of flavors in any way she wants. There are four flavors to choose from: Apple, Banana, Chico, and Durian. How many possible combination of flavors can Issa make?

In the problem, Issa can choose any number of flavors and any combination. She can choose plain milk, choose one flavor at a time, two flavors at a time, three flavors at a time, or four flavors at a time as shown in the table below (click the table to enlarge).

Notice that in writing the list, we have exhausted the number of subsets in a set with four elements. If we let a, b, c, and d stand for avocado, banana, chico, and durian, let them be members or a set and use the set notation, we can write the subsets as follows: » Read more