## The Problem

One week five bachelors agreed to go out together to eat the 5 evening meals on Monday through Friday. It was understood that Eric would miss Friday's meal because of an out-of-town wedding at which he fervently hoped to catch the bride's garter. Each bachelor served as the host at a restaurant of his choice on a different night. Use the clues below to determine which bachelor hosted the group each night and what food he selected.
1. Carl hosted the group on Wednesday.
2. The fellows ate at a Thai restaurant on Friday.
3. Bill, who detests fish, volunteered to be the first host.
4. Dave selected a steak house for the night before one of the fellows hosted everyone at a raucous pizza parlor.

There are 2 different solutions to this logic problem given below. Each illustrates the use of one of the two standard types of solve charts. These solution examples will explain the fundamental ideas involved in solving LPs. For more advanced solution stategies, both new and experienced solvers may find Tips for Solving Logic Problems to be helpful.

## Solution 1

The first step is to carefully read the entire problem statement. This usually consists of an Introduction followed by a series of numbered Clues. The Introduction frequently contains significant information that is not mentioned in the Clues. For example, from the above Introduction one can conclude that Eric was NOT Friday's host. The end of the Introduction usually clearly specifies the objective of the problem. For example, in the above problem the solver is asked to match each night of the week, Mon through Fri, with one of the 5 men and with the food he selected.

Use the provided solve charts to organize the given information and to deduce conclusions. The goal is to isolate the solution by elimination of all other possibilities. This solution demonstrates the use of a "Criss-Cross Grid" solve chart. An "X" is used to indicate that a possibility has been ruled out, and an "O" is used to indicate that a possibility has been deduced to be true.

 HOST FOOD ANDY BILL CARL DAVE X O X X X X X X X X X O X X X X X X X X X X X X X O X X X X X X O X X X
1. According to the Introduction, Eric was NOT Friday's host. Put an "X" in the box at the intersection of the "Fri" row and the "ERIC" column to show that this possibility has been eliminated.
2. Enter an "O" in the box in the "Wed" row and the "CARL" column to show that Carl is Wednesday's host (Clue 1). Enter an "X" in the other 4 host boxes in the "Wed" row (only 1 host per day and Carl is the one for Wed), and an "X" in the other 4 day boxes in the "CARL" column (since Carl only hosts 1 day).
3. Similarly based on Clue 2, enter an "O" in the "Fri-THAI" box and an "X" in each of the 4 remaining boxes in the "Fri" food row and the "THAI" column.
4. Put an "X" in the "Fish-BILL" box (Clue 3).
5. Put an "O" in the "Mon-BILL" box (Clue 3) and an "X" in the remaining host boxes in that row and column.
6. Put an "O" in the "Steak-DAVE" box (Clue 4) and an "X" in the remaining food boxes in that row and column.
At this point we will continue with a fresh copy of the criss-cross grid below in order to facilitate the reader's following the addition of more information to the chart.

 HOST FOOD ANDY BILL CARL DAVE X O X X X X X X O X X X X O X X X O X X X X O X X X O X X X X X X X O O X X X X O X X X X X X X X O X X X X X X O X X X
1. By Clue 4, Dave hosted the night before pizza. The last possible night for pizza according to the chart is Thu, and the only prior night Dave could host according to the chart is Tue. Therefore Dave hosts steak on Tue. Enter an "O" in the "Tue-DAVE" and "Tue-STEAK" boxes and "X" out the remaining boxes in those rows and columns.
(Entered in Red.)
2. By Clue 4, pizza followed steak which is on Tue. Therefore, enter an "O" in the "Wed-PIZZA" box and an "X" in the remaining boxes in that row and column.
(Entered in Blue.)
3. From the chart one sees that Eric must host on Thu and Friday's host must be Andy.
(Entered in Blue.)
4. By the chart, Mon's dinner was fish or tacos. Since it was hosted by Bill, it cannot be fish (Clue 3 or chart). Therefore Mon was tacos. The only possibility left for Thu is fish.
(Entered in Yellow.)

DAYHOSTFOOD
MonBillTacos
TueDaveSteak
WedCarlPizza
ThuEricFish
FriAndyThai
The solution to the problem can now be read off of the chart. It is displayed in table form at the left.

## Solution 2

This second solution demonstrates the use of a "Fill-In Table" solve chart.

"FILL-IN TABLE"
SOLVE CHART
DAYHOSTFOOD
MonBillTacos
TueDaveSteak
WedCarlPizza
ThuEricFish
FriAndyThai
1. Enter the 5 weekdays, Carl as Wed's host (Clue 1), Thai food on Fri (Clue 2), and Bill as Mon's host (Clue 3). (Black Entries)
2. Pizza must be Thu night or earlier. The only available row for Dave-Steak which precedes pizza (Clue 4) is Tue. Thus Pizza is Wed. (Red Entries)
3. Fish must be Thu (Clue 3) and therefore Tacos are Mon. (Blue Entries)
4. Eric cannot be Fri (Intro) and so must be Thu. Andy alone remains for Fri. (Yellow Entries)
It is evident that Solution 2 is much simpler than Solution 1. It is frequently the case that one of the solve charts is a better aid in solving a given problem than the other. In fact, sometimes one of the charts is of no help in solving. This also varies with the solver.

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