Real Mathematics: Game #3

Chocolate Box

A dear friend of mine started a new business recently. I bought a box of chocolate with the intention of visiting his store. Eventually I did visit his store. Although I could not stop myself opening the box before my visit. In the end I murdered almost half of the box. Sorry matey!

Today I checked what is left in the box and I realized something: Why aren’t same types of chocolates in the adjacent compartments?


Being Neighbors

In order to avoid neighborhood between same types of chocolates, we should be careful not to place them as shown in the photo.


Let’s call this rule “sufficient chocolate density”, or “S.C.D.”.

Question 1: Assume that you have four different types of chocolates and seven chocolates from each type. Could you have S.C.D. in such a box like the following photo?

Question 2: What is the least number of different chocolate types you can place inside this box?

Question 3: In case you have a box like shown below, at least how many different types of chocolate do you need to maintain S.C.D.?


Question 4: If you had four different chocolate types and nine from each type, could you be able to construct a box that has S.C.D.? If yes, what would it look like?

M. Serkan Kalaycıoğlu

Real Mathematics: Game #2

In school, mathematics is being used to help kids gain problem-solving skills. Even though I love arithmetic aspect of it, problem-solving is usually focused on arithmetic more than developing strategies for the problem itself. This causes kids to focus on the answer and act without thinking. I can’t emphasis this more: Thinking is integral if you’d like to learn mathematics.

When a kid solves all 100 problems from his/her math textbook, it really doesn’t tell much about his/her problem-solving skills. It only shows that kid knows how to do arithmetic. Unfortunately for that kid, arithmetic is not enough when he/she will face an original problem in future.

Space Racing

Creating new strategies has a positive impact on problem-solving. In order to achieve that one should stop worrying about arithmetic so much and focus on thinking about the problem itself.

Boşluk yarışı

It is very important to show kids problems that don’t include arithmetic within themselves. Space Racing is a kind of game that looks like it has nothing to do with mathematics. But in truth, it is a real mathematics problem. You should always remember this: a math answer can be just a paragraph.

Space Racing is a multiplayer game which requires only a paper and a pen. Players put X on empty boxes in order. Player A wins if the last two empty boxes are adjacent. Player B wins if the last two empty boxes are apart from one another.

There are so much to think about this problem:

  • Does it matter if player A starts first or not?
  • Does it matter how many empty boxes there are in the drawing?
  • Would anything change if players put two Xs in each turn?
  • Is there a strategy for player A to maximize his/her chances to win the game?
  • Is there a strategy for player B to maximize his/her chances to win the game?
  • Would it be possible to guess the outcome of the game after certain number of turns?


M. Serkan Kalaycıoğlu