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Logic Puzzle Solution

We are tasked with determining the grade and favorite color of four children: Amanda, Bill, Cathy, and Dorothy. Each child is in one of the grades (1st, 2nd, 3rd, or 4th) and has a unique favorite color (blue, red, pink, or green). We will use the provided clues to solve the puzzle.

#### Clues:
1. The 4th grader is a boy who does not like pink.
2. Dorothy is the youngest and likes blue.
3. Cathy is one grade ahead of Amanda.
4. The 2nd grader likes red.

#### Step-by-Step Solution:

##### Step 1: Analyze Clue 2
- Clue 2: Dorothy is the youngest and likes blue.
- Since Dorothy is the youngest, she must be in the 1st grade.
- Dorothy's favorite color is blue.
- Fill in the table:
- Dorothy: 1st grade, Blue.

##### Step 2: Analyze Clue 1
- Clue 1: The 4th grader is a boy who does not like pink.
- The 4th grader is a boy, so it cannot be Amanda (female).
- The 4th grader does not like pink, so the 4th grader's favorite color is either blue, red, or green.
- Since Dorothy already has blue, the 4th grader's favorite color must be red or green.
- Possible candidates for the 4th grader are Bill or Cathy (since they are boys).

##### Step 3: Analyze Clue 4
- Clue 4: The 2nd grader likes red.
- The 2nd grader's favorite color is red.
- Since Dorothy (1st grade) likes blue, and the 4th grader's favorite color is either red or green, the 2nd grader must be someone else.
- Possible candidates for the 2nd grader are Amanda, Bill, or Cathy.
- Since the 4th grader cannot like red (from Clue 1), the 2nd grader must be the one who likes red.
- Fill in the table:
- 2nd grade: Red.

##### Step 4: Analyze Clue 3
- Clue 3: Cathy is one grade ahead of Amanda.
- If Cathy is one grade ahead of Amanda, then:
- If Amanda is in the 1st grade, Cathy is in the 2nd grade.
- If Amanda is in the 2nd grade, Cathy is in the 3rd grade.
- If Amanda is in the 3rd grade, Cathy is in the 4th grade.
- From Clue 2, Dorothy is in the 1st grade, so Amanda cannot be in the 1st grade.
- From Clue 4, the 2nd grader likes red, so Amanda cannot be in the 2nd grade (because Cathy is one grade ahead of Amanda).
- Therefore, Amanda must be in the 3rd grade, and Cathy must be in the 4th grade.
- Fill in the table:
- Amanda: 3rd grade.
- Cathy: 4th grade.

##### Step 5: Determine Amanda's Favorite Color
- Amanda is in the 3rd grade.
- The 4th grader (Cathy) does not like pink (from Clue 1), so Amanda's favorite color cannot be pink.
- Dorothy likes blue (from Clue 2), so Amanda's favorite color cannot be blue.
- The 2nd grader likes red (from Clue 4), so Amanda's favorite color cannot be red.
- Therefore, Amanda's favorite color must be green.
- Fill in the table:
- Amanda: 3rd grade, Green.

##### Step 6: Determine Cathy's Favorite Color
- Cathy is in the 4th grade.
- The 4th grader does not like pink (from Clue 1), so Cathy's favorite color cannot be pink.
- Dorothy likes blue (from Clue 2), so Cathy's favorite color cannot be blue.
- The 2nd grader likes red (from Clue 4), so Cathy's favorite color cannot be red.
- Therefore, Cathy's favorite color must be green.
- However, Amanda already has green, so there is a contradiction. Let's re-evaluate:
- Since Amanda is in the 3rd grade and likes green, Cathy (in the 4th grade) must like red or green.
- But since the 2nd grader likes red, Cathy must like green.
- Correcting the previous step: Amanda must like pink.
- Fill in the table:
- Amanda: 3rd grade, Pink.
- Cathy: 4th grade, Green.

##### Step 7: Determine Bill's Grade and Favorite Color
- Bill is the only remaining child.
- Bill must be in the 2nd grade (since the 2nd grader likes red).
- Bill's favorite color is red (from Clue 4).
- Fill in the table:
- Bill: 2nd grade, Red.

#### Final Table:
| | 1st | 2nd | 3rd | 4th | Blue | Red | Pink | Green |
|---------|-----|-----|-----|-----|------|-----|------|-------|
| Amanda | | | X | | | | X | |
| Bill | | X | | | | X | | |
| Cathy | | | | X | | | | X |
| Dorothy | X | | | | X | | | |

#### Final Answer:
- Amanda: 3rd grade, Pink.
- Bill: 2nd grade, Red.
- Cathy: 4th grade, Green.
- Dorothy: 1st grade, Blue.

$$
\boxed{
\begin{array}{ll}
\text{Amanda: 3rd grade, Pink} \\
\text{Bill: 2nd grade, Red} \\
\text{Cathy: 4th grade, Green} \\
\text{Dorothy: 1st grade, Blue}
\end{array}
}
$$