By Tauri Morrow

The game "Error Correcting Codes" is not a player one or player two game, or ever win or lose game. It is a game that has an expert of Error Correcting Codes, and a player choosing a number.

The object to "Error Correcting Codes" is for the expert of the game to be able to tell the player which number that he chose. You start out with a chart of numbers, some black and some bold like so:

57 42 26 24 17 61

67 72 16 14 27 51

7 12 76 74 47 31

46 53 37 35 6 70

45 50 34 36 5 73

43 56 32 30 3 75

The player of the game is supposed to choose a number of their choice. Then the player tells the expert the colors of the numbers in the column that they chose, but the trick is that the player lies about the color of the number that they chose. For example, if the number that the player chose was the number "3", the player would tell the expert; bold, bold, bold, black, black, bold. Telling a fib a bout the color of the number "3", which was black. From the information that the player told the expert, the expert should be able to tell the player the number that in which they picked, which was the number "3".

The player is probably asking himself or herself, " How is it possible for the expert to know he number that the player picked, just by telling them colors?" At first, the player is definitely going to think that the expert has memorized the colors and the numbers of each column, but that is definitely no true. The expert does everything by mathematics, to get the number that the player has chosen.

First of all, to become an expert of "Error Correcting Codes, the expert must understand the binary representation of numbers. Binary representation is a representation in base two whit ascending powers of two form right to left, beginning with 2^0, which is defined as 2 to the 0 power. This is how you show binary representation:

After understanding the process of binary representation, you use binary configuration to nim add the represented number in base 2. For example, if you wanted to nim add the numbers two and three, which are represented binaurally as 3=11, and 2=10. Here's how you would add them:

10

+11

----

101

When you use binary configuration, 1 plus 1 equals 10, and 0

Plus 1 equals 1.

HOW TO MAKE AN ERROR CORRECTING CODE CHART

I'm going to explain how to make a chart in base two

and base three.

MAKING A BASE TWO CHART

First of all you have to decide what you want bold and black to represent. They can either be represented as a one or a zero. So let's say bold is represented as a one, and black is represented as a zero.

Before beginning to make the chart, you have to decide what the colors of your columns are going to be. I want mine to be, R=bold, and B=black.

B R B R

B R B R

B R B R

B R R B

Then after coming up with a pattern, you use binary

Configuration to get the numbers in the chart.

8 B 0 B 0 B 0 R 1

4 B 0 B 0 R 1 B 0

2 B 0 R 1 B 0 B 0

1 R 1 B 0 B 0 B 0

1 2 4 8

8 R 1 R 1 R 1 B 0

4 R 1 R 1 B 0 R 1

2 R 1 B 0 R 1 R 1

1. B 0 R 1 R 1 R 1

8 B 0 B 0 B 0 R 1

4 B 0 B 0 R 1 B 0

2 B 0 R 1 B 0 B 0

1 B 0 R 1 R 1 R 1

8 R 1 R 1 R 1 B 0

4 R 1 R 1 B 0 R 1

2 R 1 B 0 R 1 R 1

1 R 1 B 0 B 0 B 0

15 12 10 6

This is the base two chart that is made:

8 7 9 6

4 11 5 10

2 13 3 12

1 14 0 15

MAKING A BASE THREE CHART

Using the same color pattern as the base two chart,

this is how you make a base three chart:

27 B 0 B 0 B 0 R 1

9 B 0 B 0 R 1 B 0

3 B 0 R 1 B 0 B 0

1 R 1 B 0 B 0 B 0

1 3 9 27

27 R 1 R 1 R 1 B 0

9 R 1 R 1 B 0 R 1

3 R 1 B 0 R 1 R 1

1 B 0 R 1 R 1 R 1

39 37 31 13

27 B 0 B 0 B 0 R 1

9 B 0 B 0 R 1 B 0

3 B 0 R 1 B 0 B 0

1 B 0 R 1 R 1 R 1

0 4 10 28

27 R 1 R 1 R 1 B 0

9 R 1 R 1 B 0 R 1

3 R 1 B 0 R 1 R 1

1 R 1 B 0 B 0 B 0

40 36 30 12

This is the base three chart that is made:

27 13 28 12

9 31 10 30

3 37 4 36

1 39 0 40