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.

Based on all the clues we know that some eat ham, some have sausage and some bacon, so there

are exactly two of each meat, because Mrs. F won't cook any item for just one. Same with

the beverages.

Looking only at #6, we know the following

The sausage eaters have tea, so

entree([e]gg,[p]ancake)/meat([b]acon,[h]am,[s]ausage)/beverage([c]offee,[t]ea,[m]ilk)
?st
?st

since all meals are different then one st has pancakes, the other eggs, so

est
pst

From #6, we can fill in most of the rest of the meals

est
pst
p?c
p?c
??m
??m

Bob drinks coffee (#5), and has Ham (#2), so

est
pst
phc - Bob
p?c
??m
??m

Again, since no two meals are exactly alike, and there are exactly 2 of each meat we can

fill in much of the rest

est
pst
phc - Bob
pbc
?bm
?hm

There are more than 2 eggs (#7), so the last two had to be eggs

est
pst
phc - Bob
pbc
ebm
ehm

The other ham was Chuck, from #2, so

est
pst
phc - Bob
pbc
ebm
ehm - Chuck


Al doesn't eat sausage, so he is either pbc or ebm, BUT Al sit's next to the boarder who

eats bacon and pancakes (pb?), so Al eats ebm, NOT pbc

est
pst
phc - Bob
pbc
ebm - Al
ehm - Chuck

Ned doesn't like pancakes, so he is est

est - Ned
pst
phc - Bob
pbc
ebm - Al
ehm - Chuck


Peter doesn't like Bacon, so he must be pst. And Will fills in the last spot.

est - Ned
pst - Peter
phc - Bob
pbc - Will
ebm - Al
ehm - Chuck


Why do these things sound so much easier when you write them than when you actually do them?

Posted by Lawrence on 2003-08-24 10:51:13