Preparing breakfast for Will and her five other boarders before they set out for work each morning keeps Mrs. Finnegan very busy. Her task is made somewhat easier, however, by the fact that each young man has the same breakfast every morning---either eggs or pancakes, accompanied by either bacon, ham, or sausage. Each one also has either coffee, tea, or milk. No two have exactly the same breakfast. It should be added that Mrs. Finnegan has a firm rule: She will not prepare any dish for only one person. From the following clues can you determine what each boarder has for breakfast?

1. Al, who does not like sausage, usually sits next to the boarder who breakfasts on bacon and pancakes.

2. Bob and Chuck both have ham.

3. Peter does not care for bacon.

4. Ned does not like pancakes.

5. Bob has coffee.

6. The sausage eaters have tea; two of the pancake eaters have coffee; the other two boarders drink milk.

7. More than two of the boarders have eggs.

Al: Eggs, bacon, and milk
Bob: Pancakes, ham, and coffee
Chuck: Eggs, ham, and milk
Ned: Eggs, sausage, and tea
Peter: Pancakes, sausage, and tea
Will: Pancakes, bacon, and coffee

Method:
There are six boarders altogether.

There are two tea drinkers, two coffee drinkers, and two milk drinkers (6).

Also, since there are three different sides, and Mrs. Finnegan will not prepare a single dish for any one person, there must be two people who have each.

More than two of them pancakes (6), and more then two of them have eggs (7), so there must be three who have each:

P


P


P


E


E


E

Both of the sausage-eaters have tea (6).
Since no two people have exactly the same breakfast, one must have eggs and the other pancakes.

P  S  T


P


P


E  S  T


E


E

That takes care of one of the "pancake-eaters."
The other two boarders with pancakes must both have coffee (6), so one must have ham and one bacon.

P  S  T


P  H  C


P  B  C


E  S  T


E


E

The last two boarders both have eggs.
Also, they both have milk milk, so again, one must have ham and one has bacon.

P  S  T


P  H  C


P  B  C


E  S  T


E  H  M


E  B  M

Now to figure out who has what meal.
Bob has ham (2) and coffee (5); he must be the second boarder with pancakes.

P  S  T


P  H  C - Bob


P  B  C


E  S  T


E  H  M


E  B  M

Chuck is the other boarder with ham:

P  S  T


P  H  C - Bob


P  B  C


E  S  T


E  H  M - Chuck


E  B  M

Al does not like sausage (1).
He is also not the boarder with pankcakes and bacon (and coffee) (1). Therefore, he must have eggs, bacon, and milk:

P  S  T


P  H  C - Bob


P  B  C


E  S  T


E  H  M - Chuck


E  B  M - Al

Ned, who does not like pancakes (4), is the last person with eggs.

P  S  T


P  H  C - Bob


P  B  C


E  S  T - Ned


E  H  M - Chuck


E  B  M - Al

Finally, Peter does not like bacon (3).
He must be the remaining boarder with sausage, and Will, who isn't picky, has pancakes and bacon:

P  S  T - Peter


P  H  C - Bob


P  B  C - Will


E  S  T - Ned


E  H  M - Chuck


E  B  M - Al

In sum, here's what each has:

Al: Eggs, bacon, and milk
Bob: Pancakes, ham, and coffee
Chuck: Eggs, ham, and milk
Ned: Eggs, sausage, and tea
Peter: Pancakes, sausage, and tea
Will: Pancakes, bacon, and coffee
Edited on August 25, 2003, 10:03 pm

Posted by DJ on 2003-08-23 12:56:13