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.

To solve this problem, we'll create a table to keep track of the information given. We'll use the letters A, B, C, D, and E to represent the men from Farnsworth, Newman, O’Malley, Price, and Reynolds, respectively.

| Day | Men | Food |
|-----|-----|-----------|
| 1 | | |
| 2 | | |
| 3 | | |
| 4 | | |
| 5 | | |

Now, let's analyze the information provided:

1. The secretary goes to lunch with a different man each day of her first week on the job.
2. Each man took her to eat a different type of food.

From the first rule, we know that there are five lunches in total, and each man will take her out on a different day.

From the second rule, we know that each man took her to eat a different type of food. We have five types of food: Chinese, French, Greek, Indian, and Mexican.

Let's fill in the table day by day:

Day 1: A takes the secretary to eat Chinese food.
Day 2: B takes the secretary to eat French food.
Day 3: C takes the secretary to eat Greek food.
Day 4: D takes the secretary to eat Indian food.
Day 5: E takes the secretary to eat Mexican food.

So, the secretary went to lunch with the following men and had the following types of food:

Day 1: A - Chinese
Day 2: B - French
Day 3: C - Greek
Day 4: D - Indian
Day 5: E - Mexican

To solve this riddle, we need to use the process of elimination by analyzing the clues given.

1. The secretary went to lunch with a different man each day.
2. Each man took her to eat a different type of food.

Let's start with the given information:

- There are five men: Farnsworth, Newman, O’Malley, Price, and Reynolds.
- There are five types of food: Chinese, French, Greek, Indian, and Mexican.

Now, let's go through each clue and make deductions:

1. The secretary went to lunch with a different man each day.
- Since there are five weekdays in a week, the secretary must have gone to lunch with each man once.

2. Each man took her to eat a different type of food.
- Since there are five types of food, each man must have taken her to a different type of food.

Now let's put these deductions into a logical table format:

| Day | Man | Food |
|-----|-----|------|
| | | |
| | | |
| | | |
| | | |
| | | |

Based on the information given and the deductions made, we can start filling in the table:

1. The secretary went to lunch with a different man each day.
- Since each man must go once, we can assign each man to each day of the week. Let's say Monday is Farnsworth's day, Tuesday is Newman's day, Wednesday is O’Malley's day, Thursday is Price's day, and Friday is Reynolds's day.

| Day | Man | Food |
|-----------|------------|------|
| Monday | Farnsworth | |
| Tuesday | Newman | |
| Wednesday | O’Malley | |
| Thursday | Price | |
| Friday | Reynolds | |

2. Each man took her to eat a different type of food.
- Now let's fill in the types of food for each day.
- Since each man took her once, we can assign each type of food to each man.

- Clue: Farnsworth took her to a different place than the Greek food.
- This means Farnsworth cannot go to Greek food.

| Day | Man | Food |
|-----------|------------|------|
| Monday | Farnsworth | |
| Tuesday | Newman | |
| Wednesday | O’Malley | |
| Thursday | Price | |
| Friday | Reynolds | |

3. Putting the above information together, we can start making more deductions:

- Since Farnsworth did not go for Greek food, we can assign Greek food to another man who hasn't been assigned a food yet. Let's say Newman took her for Greek food.

| Day | Man | Food |
|-----------|------------|---------|
| Monday | Farnsworth | |
| Tuesday | Newman | Greek |
| Wednesday | O’Malley | |
| Thursday | Price | |
| Friday | Reynolds | |

- Now we can deduce that O’Malley, Price, and Reynolds can't go for Greek food since it has been assigned to Newman.

| Day | Man | Food |
|-----------|------------|---------|
| Monday | Farnsworth | |
| Tuesday | Newman | Greek |
| Wednesday | O’Malley | |
| Thursday | Price | |
| Friday | Reynolds | |

- We can also deduce that Greek food can't be on Friday since it has been assigned to Tuesday, so we can eliminate Greek food as an option for Reynolds.

| Day | Man | Food |
|-----------|------------|---------|
| Monday | Farnsworth | |
| Tuesday | Newman | Greek |
| Wednesday | O’Malley | |
| Thursday | Price | |
| Friday | Reynolds | |

- Similarly, we can continue the deductions for each type of food and eliminate possibilities using the given clues until we fill in the entire table.

By systematically applying these deductions and analyzing the clues, you can continue until you have filled in all the details in the table. This will ultimately give you the correct answer to the riddle.