The Braille system uses uses _____ different dot patterns, where each pattern consists of dots arranged in a grid of two columns and three rows.

Options

A. 70
B. 63
C. 72
D. 56

Answer

To solve the question about the Braille system, we need to understand how it is structured. The Braille system is designed for visually impaired individuals to read through touch. Here's a step-by-step breakdown:

### Step-by-Step Solution:

1. **Understanding the Braille System**: The Braille system uses a grid format for its characters, which consists of two columns and three rows. Each character is represented by a unique pattern of raised dots.

**Hint**: Think about how the arrangement of dots can create different characters.

2. **Counting the Dots**: In the Braille grid, there are a total of 6 positions for dots (2 columns x 3 rows = 6 positions). Each position can either be filled with a dot or left empty.

**Hint**: Consider how many combinations can be made with 6 positions where each can be filled or not filled.

3. **Calculating Possible Patterns**: Each of the 6 positions can be either a dot or not a dot. Therefore, the total number of different combinations of dots (or patterns) can be calculated using the formula for combinations of binary choices (2 options for each position).

**Hint**: Use the formula \(2^n\) where \(n\) is the number of positions (in this case, 6).

4. **Finding the Total Combinations**: Using the formula:
\[ 2^6 = 64 \]
This means there are 64 possible combinations of dots.

**Hint**: Remember that one of these combinations represents the absence of dots, which is not used in the Braille system for letters.

5. **Excluding the Empty Pattern**: Since one of these combinations is just an empty cell (no dots), we subtract this from the total:
\[ 64 - 1 = 63 \]

**Hint**: Think about what the empty pattern represents and why it doesn't count as a character.

6. **Conclusion**: Therefore, the Braille system uses 63 different dot patterns, where each pattern consists of dots arranged in a grid of two columns and three rows.

**Final Answer**: The Braille system uses **63** different dot patterns.