A popular new secretary at the law firm of Farnsworth, Newman, O’Malley, Price, and Reynolds, is taken to lunch by a different one of those five men on each of her first week on the job. Each man took her to eat at a different one of these five types of food: Chinese, French, Greek, Indian, and Mexican. From the information given, determine whom she went to lunch with on each day and the type of food that they had. 1. Neither Mr. Newman nor Mr. Reynolds took her to lunch on Thursday or Friday but one took her for Chinese food and the one who took her lunch earlier than the other her for Greek food. 2. She went for a Mexican food lunch before her Indian food lunch but after her lunch with Mr. Price. 3. She had lunch with Mr. Farnsworth before her lunch with Mr. O’ Malley but after the lunch when she French food, which was not on Monday. 4. She has lunch with Mr. Newman later in the week than than the lunch when she had French food.

To solve this problem, we will create a grid with the days of the week and the types of food. We will add the names of the men as we gather more information.

First, let's list the possible options for each category:
- Days of the week: Monday, Tuesday, Wednesday, Thursday, Friday
- Types of food: Chinese, French, Greek, Indian, Mexican
- Men's names: Farnsworth, Newman, O’Malley, Price, Reynolds

Now let's analyze each statement and fill in the grid accordingly:

Statement 1: Neither Mr. Newman nor Mr. Reynolds took her to lunch on Thursday or Friday, but one took her for Chinese food and the one who took her lunch earlier than the other took her for Greek food.

- From this statement, we know that Mr. Newman and Mr. Reynolds didn't take her to lunch on Thursday or Friday.
- We also know that one of them took her for Chinese food and the other for Greek food, with the one who took her lunch earlier choosing Greek food.

Statement 2: She went for a Mexican food lunch before her Indian food lunch but after her lunch with Mr. Price.

- From this statement, we know that she went for a Mexican food lunch before her Indian food lunch.
- We also know that her lunch with Mr. Price was before her Mexican food lunch.

Statement 3: She had lunch with Mr. Farnsworth before her lunch with Mr. O’Malley but after the lunch where she had French food, which was not on Monday.

- From this statement, we know that she had lunch with Mr. Farnsworth before her lunch with Mr. O’Malley.
- We also know that her lunch with French food was not on Monday.

Statement 4: She had lunch with Mr. Newman later in the week than the lunch when she had French food.

- From this statement, we know that she had lunch with Mr. Newman later in the week than the lunch with French food.

Using the above information, let's start filling out the grid:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | |
| French | | | | | |
| Greek | | | | | |
| Indian | | | | | |
| Mexican| | | | | |

From statement 3, we know that French food wasn't on Monday. Let's mark that in the grid:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | |
| French | | | | | X |
| Greek | | | | | |
| Indian | | | | | |
| Mexican| | | | | |

From statement 1, we know that Mr. Newman or Mr. Reynolds took her to lunch for Chinese and Greek food. Also, the one who took her lunch earlier chose Greek food. Let's fill that in the grid:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | X |
| French | | | | | X |
| Greek | | | | | |
| Indian | | | | | |
| Mexican| | | | | |

From statement 3, we know that she had lunch with Mr. Farnsworth before Mr. O’Malley. Let's fill that in:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | X |
| French | | | | | X |
| Greek | | | | | |
| Indian | | | | | |
| Mexican| | | | | |

From statement 2, we know that she had her lunch with Mr. Price before her Mexican food lunch. Let's fill that in:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | X |
| French | | | | | X |
| Greek | | | | | |
| Indian | | | | | |
| Mexican| | | X | | |

From the same statement, we also know that her Indian food lunch was before the Mexican food lunch. Let's fill that in as well:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | X |
| French | | | | | X |
| Greek | | | | | |
| Indian | | | X | | |
| Mexican| | | X | | |

Finally, from statement 4, we know that she had lunch with Mr. Newman later in the week than the lunch with French food. Let's fill that in:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | X |
| French | | | | | X |
| Greek | | | | | |
| Indian | | | X | | |
| Mexican| | | X | | |

Now, let's analyze the grid and determine the correct solutions:
- The lunch with Greek food is on Friday, so either Mr. Newman or Mr. Reynolds took her to lunch on Friday.
- The lunch with French food is after Wednesday, so it could be on Thursday or Friday. However, it cannot be on Thursday because Mr. Newman and Mr. Reynolds didn't take her to lunch on Thursday. Therefore, the lunch with French food is on Friday, and Mr. Newman took her to lunch that day.
- The lunch with Mr. Newman is later in the week than the lunch with French food. Since the lunch with French food is on Friday, the lunch with Mr. Newman must be on Friday as well.

Using this information, we can fill in the final grid:

| | Monday | Tuesday | Wednesday | Thursday | Friday |
|--------|--------|---------|-----------|----------|--------|
| Chinese| | | | | X |
| French | | | | | X |
| Greek | | | | | X |
| Indian | | | X | | |
| Mexican| | | X | | |

Now let's go through the remaining statements to fill in the missing information:

From statement 1, the man who took her for Chinese food took her lunch earlier than the one who took her for Greek food. Since Mr. Newman took her for Chinese food and Mr. Reynolds took her for Greek food, Mr. Newman's lunch must be earlier than Mr. Reynolds's.

Therefore, the final solution is:
- Monday: Mr. Farnsworth, French food
- Tuesday: Mr. O’Malley, Mexican food
- Wednesday: Mr. Price, Indian food
- Thursday: Mr. Newman, Chinese food
- Friday: Mr. Reynolds, Greek food