Real Mathematics: Game #1

Circle of Numbers

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Most of the countries in the world use these symbols for the remarkable decimal system. The system was designed so perfect, even though symbols might change in some regions, logic of the system is conserved all around the world. Decimal system is one of those things that are “universal”.

If you are willing to participate in today’s modern world, you’d better know how to use numbers. You could go on and try to live a day without using any numbers: You’d see that it is impossible to finish even one single day. Actually, using numbers is not enough: you should be able to understand what a given number represents.

Understanding Numbers

What do I mean by “understanding numbers”?

If I show you 2125555555, can you associate it with anything?

How about 212 555 55 55?

Now most of you realize that 212 555 55 55 is a telephone number. Using three blank spaces inside the number 2125555555 changed the way you look at it.

Numbers take too much space in our daily lives. I think this is a great reason to work and develop a good understanding of them. Circle of Numbers is a game that helps children cultivate the ability of using numbers.

In order to play Circle of Numbers, all you need is a pencil and a pen. This game can have various numbers of versions.

Circle of Numbers 1.0.0

Draw a circle.

Place four boxes on the circle.

You have to place the numbers 0, 1, 2 and 3 inside the boxes such that difference of two adjacent boxes will be an odd number.

Example

Circle of Numbers 1.0.1

Again draw a circle with four boxes on it.

This time each of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 should be used.

In order to do that, you will need ten boxes which means you will have to add six more boxes on the circle.

Difference of two adjacent boxes should be odd.

Example

Let’s assume 4 and 7 are placed as following.

Player knows no matter which number is chosen, there will be number pairs that will not have odd difference. For instance if 5 is chosen, even though 5-4=1 is odd, 7-5=2 will be even. Player should add a new box to avoid this problem. Following will show you a working strategy step-by-step.

Circle of Numbers 2.0.0

Assume that there are five boxes on the circle and you are allowed to use the numbers 1, 3, 5, 8, 9. Can you construct a valid circle?

Check it out

I just gave three different versions for the game Circle of Numbers with three different names: Circle of Numbers 1.0.0, Circle of Numbers 1.0.1 and Circle of Numbers 2.0.0. What do these numbers remind you? What would Circle of Numbers 2.0.1 look like?

M. Serkan Kalaycıoğlu