Question
A game is played by moving 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
5
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
5
Answers
GPT-4o mini
Let's analyze the game step by step, starting with the game piece placed on the rightmost black space.
### Step 1
- **Initial Position:** The game piece starts on the rightmost black space, which we represent as position 9 (0-based index).
- **Counter:** Set to 0.
### Step 2
- Since the game piece is on a **black** space (position 9), according to the algorithm, we move the game piece 1 position to the left.
- **New Position:** Position 8 (which is a yellow space).
### Step 3
- Increase the counter by 1.
- **Counter:** 1.
### Step 4
- Checking the position of the game piece:
- It's on a **yellow** space, so we go back to Step 2.
### Step 2
- Now the game piece is on a **yellow** space (position 8).
- We move the game piece 3 positions to the left.
- **New Position:** Position 5 (which is a red space).
### Step 3
- Increase the counter by 1.
- **Counter:** 2.
### Step 4
- Now the game piece is on the **red** space.
- Since we have landed on the red space, the game is complete.
Thus, the final value of the counter at the end of the game is **2**.
**Option A: 2** is the correct answer.
### Step 1
- **Initial Position:** The game piece starts on the rightmost black space, which we represent as position 9 (0-based index).
- **Counter:** Set to 0.
### Step 2
- Since the game piece is on a **black** space (position 9), according to the algorithm, we move the game piece 1 position to the left.
- **New Position:** Position 8 (which is a yellow space).
### Step 3
- Increase the counter by 1.
- **Counter:** 1.
### Step 4
- Checking the position of the game piece:
- It's on a **yellow** space, so we go back to Step 2.
### Step 2
- Now the game piece is on a **yellow** space (position 8).
- We move the game piece 3 positions to the left.
- **New Position:** Position 5 (which is a red space).
### Step 3
- Increase the counter by 1.
- **Counter:** 2.
### Step 4
- Now the game piece is on the **red** space.
- Since we have landed on the red space, the game is complete.
Thus, the final value of the counter at the end of the game is **2**.
**Option A: 2** is the correct answer.