BACHELOR BINGE
Logic Problem
William T. Pelletier
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.
- Carl hosted the group on Wednesday.
- The fellows ate at a Thai restaurant on Friday.
- Bill, who detests fish, volunteered to be the first host.
- Dave selected a steak house for the night before one of the fellows hosted everyone at a raucous pizza parlor.
HOST / FOOD
A
N
D
Y / B
I
L
L / C
A
R
L / D
A
V
E / E
R
I
C / F
I
S
H / P
I
Z
Z
A / S
T
E
A
K / T
A
C
O
S / T
H
A
I
D
A
Y / Mon
Tue
Wed
Thu
Fri
F
O
O
D / Fish
Pizza
Steak
Tacos
Thai
"CRISS-CROSS GRID"
SOLVE CHART
/ DAY / HOST / FOOD
"FILL-IN TABLE"
SOLVE CHART
Use one of these tables to solve your problem.
Tips for Solving Logic ProblemsLogic problems are entertaining opportunities to practice thinking clearly and to enjoy the fruits of such activity. A logic problem consists of a jumble of facts and relationships from which one must deduce an organized structure. The best way to learn how to solve such problems is to try it oneself or to work through an example. After having worked through this example or tried others, the following more general tips may be of help.
- Carefully read the entire problem. This usually consists of an Introduction followed by a series of numbered Clues. Clues are often hidden in the Introduction. The Introduction also clearly specifies the objective of the problem. It is important to have this objective clearly in mind before attempting to unravel the problem.
- Use criss-cross grids or fill-in tables to organize the given information and to deduce conclusions. The goal is to isolate the solution by the elimination of all other possibilities. It is frequently the case that one type of solve chart is a better aid in solving a given problem than another. Thus if one is stuck, try using a different solve chart or diagram to look at the puzzle from an alternative point of view. Frequently it's profitable to use both types of solve charts in conjunction with each other. Occasionally for very difficult logic problems, one may need to use many charts representing various portions of the problem.
- Instead of placing an "X" in a criss-cross grid to eliminate a possibility, put the number of the clue used to eliminate it. This can be very helpful part way through a problem when one is trying to correct a mistake or check one's work.
- Watch for subtle gender clues based on names or pronouns.
- A clue like, "Neither Bob nor the one from Kansas drives the red car" includes the frequently overlooked information that Bob is not from Kansas.
- After having entered information from all the clues in the solve charts, reread everything in light of the charts. Frequently, you will now be able to use clues (to deduce more information) that were not usable the first time through the problem.
- Puzzle magazine editors usually consider logic problems, which require a fill-in table to be harder than those for which a criss-cross grid is sufficient. The majority of the harder logic problems tend to be table puzzles. One way to attack these puzzles is to find first a list of all the different "entities" (people or dogs or cities or whatever) involved and then enter them on the different rows of the table. Such a list will identify the entities by whatever various attributes one is supposed to match up in the puzzle.
- Order relationships are very important. For puzzles that have them, they are frequently the key to breaking open the puzzle. Sometimes comparison of order relationships will help the solver find a complete list of the "entities" involved in a puzzle (see previous tip).
- One way to get "unstuck" is to make an assumption. If possible, find one to make which has been narrowed down to 2 possibilities. Assume one of the possibilities and continue trying to solve the puzzle under that assumption. If you encounter a contradiction, then your assumption was wrong and you can proceed from there knowing the other possibility must be true. If you complete the puzzle, then your assumption was right and you have solved the problem. In testing a hypothesis, it may be helpful to switch to another writing implement or to use different symbols to distinguish the hypothesis and its corollaries from the known facts and conclusions.
- Verify your proposed solution by checking that it satisfies the introduction and all the clues.
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.
"CRISS-CROSS GRID"SOLVE CHART
HOST / FOOD
A
N
D
Y / B
I
L
L / C
A
R
L / D
A
V
E / E
R
I
C / F
I
S
H / P
I
Z
Z
A / S
T
E
A
K / T
A
C
O
S / T
H
A
I
D
A
Y / Mon / X / O / X / X / X / X
Tue / X / X / X
Wed / X / X / O / X / X / X
Thu / X / X / X
Fri / X / X / X / X / X / X / X / O
F
O
O
D / Fish / X / X
Pizza / X
Steak / X / X / X / O / X
Tacos / X
Thai / X
/
- 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.
- 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).
- 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.
- Put an "X" in the "Fish-BILL" box (Clue 3).
- Put an "O" in the "Mon-BILL" box (Clue 3) and an "X" in the remaining host boxes in that row and column.
- 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
A
N
D
Y / B
I
L
L / C
A
R
L / D
A
V
E / E
R
I
C / F
I
S
H / P
I
Z
Z
A / S
T
E
A
K / T
A
C
O
S / T
H
A
I
D
A
Y / Mon / X / O / X / X / X / X / X / X / O / X
Tue / X / X / X / O / X / X / X / O / X / X
Wed / X / X / O / X / X / X / O / X / X / X
Thu / X / X / X / X / O / O / X / X / X / X
Fri / O / X / X / X / X / X / X / X / X / O
F
O
O
D / Fish / X / X
Pizza / X
Steak / X / X / X / O / X
Tacos / X
Thai / X
/
- 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.) - 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.) - From the chart one sees that Eric must host on Thu and Friday's host must be Andy.
(Entered in Blue.) - 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.)
"FILL-IN TABLE"
SOLVE CHART
DAY / HOST / FOOD
Mon / Bill / Tacos
Tue / Dave / Steak
Wed / Carl / Pizza
Thu / Eric / Fish
Fri / Andy / Thai
/
- 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)
- 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)
- Fish must be Thu (Clue 3) and therefore Tacos are Mon. (Blue Entries)
- Eric cannot be Fri (Intro) and so must be Thu. Andy alone remains for Fri. (Green 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.