Question
ing a game piece left or right along a horizontal game board. The board consists of spaces of various colors, as shown. The circle represents the initial location of the game piece.
Yellow Black Green Green Red Yellow Black Black Yellow Black
●
The following algorithm indicates how the game is played. The game continues until the game is either won by landing on the red space or lost when the piece moves off either end of the board.
Step 1:
Place a game piece on a space that is not red and set a counter to 0.
Step 2:
If the game piece is on a yellow space, move the game piece 3 positions to the left and go to step 3. Otherwise, if the game piece is on a black space, move the game piece 1 position to the left and go to step 3. Otherwise, if the game piece is on a green space, move the game piece 2 positions to the right and go to step 3.
Step 3:
Increase the value of the counter by 1.
Step 4:
If game piece is on the red space or moved off the end of the game board, the game is complete. Otherwise, go back to step 2.
Question
7
Mark for Review
If a game is begun by placing the game piece on the rightmost black space for step 1, what will be the value of the counter at the end of the game?
2
Option A,2
3
Option B,3
4
Option C,4
Yellow Black Green Green Red Yellow Black Black Yellow Black
●
The following algorithm indicates how the game is played. The game continues until the game is either won by landing on the red space or lost when the piece moves off either end of the board.
Step 1:
Place a game piece on a space that is not red and set a counter to 0.
Step 2:
If the game piece is on a yellow space, move the game piece 3 positions to the left and go to step 3. Otherwise, if the game piece is on a black space, move the game piece 1 position to the left and go to step 3. Otherwise, if the game piece is on a green space, move the game piece 2 positions to the right and go to step 3.
Step 3:
Increase the value of the counter by 1.
Step 4:
If game piece is on the red space or moved off the end of the game board, the game is complete. Otherwise, go back to step 2.
Question
7
Mark for Review
If a game is begun by placing the game piece on the rightmost black space for step 1, what will be the value of the counter at the end of the game?
2
Option A,2
3
Option B,3
4
Option C,4
Answers
GPT-4o mini
To determine the value of the counter when starting on the rightmost black space, let's break down the movements step by step:
1. **Starting Position**: The game piece starts on the rightmost black space. The index of the spaces from left to right is:
- 0: Yellow
- 1: Black
- 2: Green
- 3: Green
- 4: Red
- 5: Yellow
- 6: Black
- 7: Black
- 8: Yellow
- 9: Black
- 10: (Game Piece)
The starting position is at index 9.
2. **Game Process**:
- **Step 2**: The piece is on a black space (index 9), so we move 1 position to the left (to index 8).
- **Step 3**: Increase the counter by 1. Counter = 1.
- **Step 2**: Now the piece is on a yellow space (index 8). Move 3 positions to the left (to index 5).
- **Step 3**: Increase the counter by 1. Counter = 2.
- **Step 2**: Now the piece is on a yellow space (index 5). Move 3 positions to the left (to index 2).
- **Step 3**: Increase the counter by 1. Counter = 3.
- **Step 2**: Now the piece is on a green space (index 2). Move 2 positions to the right (to index 4).
- **Step 3**: Increase the counter by 1. Counter = 4.
- **Step 2**: Now the piece is on a red space (index 4). The game ends because the piece is on the red space.
3. **Final Counter Value**: The counter increments were as follows: 1 (first increment), 1 (second increment), 1 (third increment), 1 (fourth increment).
- After all these moves, the counter value is 4.
Therefore, the answer is **Option C: 4**.
1. **Starting Position**: The game piece starts on the rightmost black space. The index of the spaces from left to right is:
- 0: Yellow
- 1: Black
- 2: Green
- 3: Green
- 4: Red
- 5: Yellow
- 6: Black
- 7: Black
- 8: Yellow
- 9: Black
- 10: (Game Piece)
The starting position is at index 9.
2. **Game Process**:
- **Step 2**: The piece is on a black space (index 9), so we move 1 position to the left (to index 8).
- **Step 3**: Increase the counter by 1. Counter = 1.
- **Step 2**: Now the piece is on a yellow space (index 8). Move 3 positions to the left (to index 5).
- **Step 3**: Increase the counter by 1. Counter = 2.
- **Step 2**: Now the piece is on a yellow space (index 5). Move 3 positions to the left (to index 2).
- **Step 3**: Increase the counter by 1. Counter = 3.
- **Step 2**: Now the piece is on a green space (index 2). Move 2 positions to the right (to index 4).
- **Step 3**: Increase the counter by 1. Counter = 4.
- **Step 2**: Now the piece is on a red space (index 4). The game ends because the piece is on the red space.
3. **Final Counter Value**: The counter increments were as follows: 1 (first increment), 1 (second increment), 1 (third increment), 1 (fourth increment).
- After all these moves, the counter value is 4.
Therefore, the answer is **Option C: 4**.