Logic problem construction process

Logic Problem Construction Process:
1. Decide on the general situation for the puzzle. For example, Football Fans will be
about 4 Detroit Lions football fans who attend the 1998 Super Bowl to cheer the
Lions on to victory.
2. Decide on the attributes to organize for the solution. Start small and add attributes
later if you want to increase the complexity level. For our example, the attributes
will be the names of the 4 fans, the colors of the jerseys they wore to the game,
the quarter each one left his seat to visit the concession stand, the snack each
brought back to eat, and the order they sat in their seats.
3. Decide on the "answer" to the logic problem. Here is the answer with which we
will begin.
SEAT 1 SEAT 2 SEAT 3 SEAT 4
Name Joseph Daniel Stephen Noah
Shirt Green Red Blue Yellow
Quarter 1 4 2 3
Snack Popcorn Pizza Hot Dog Nachos
4. Use a table and/or a grid chart to help you construct clues which eliminate every
possible solution except your answer. This is an iterative process in which you
may change your clues and "answer" many times. Ideas will come as you work on
this part. Experience working LPs is a big help here as an experienced solver is
familiar with many different types of clues that can be used. I will work through
this clue development process below for this problem.
5. Write up the Introduction and Clues. Clues may be hidden in the Introduction.
The Introduction should clearly specify the objective of the problem. Try to be
concise and clear; avoid ambiguity. Decide on the order in which to list the clues;
this should usually be different from the order in which they were developed in
order to disguise the constructor's thought process. If possible, have several
friends proof-read and solve the problem to check for mistakes and insure clarity.
Listen to their feedback.
6. Test your problem by checking to see that the answer satisfies the introduction
and all the clues. Work it from scratch to verify that the answer is unique and can
be determined from the clues.
Clue Development Process:
1. Start by arbitrarily selecting a clue which describes a relationship between the
attributes in the chart.
The blue-shirted fan sat next to both the red-shirted and yellow-shirted fans.
This clue narrows the arrangement of colors to 4 possibilities:
GRBY, GYBR, RBYG, and YBRG.
Future clues should work toward eliminating the 3 incorrect possibilities and
linking relationships with other attributes to fill in the remaining slots.
2. Select another relationship.
Daniel sat next to both the fan who bought a hot dog and the one who visited the
concession stand in the first quarter.
Similarly, this clue gives 4 possible fan orderings:
Q1, Dan, HD, ?
?, Q1, Dan, HD
HD, Dan, Q1, ?
?, HD, Dan, Q1.
Each of the 4 possibilities from Clue 1 may be paired with one of the 4 from Clue
2 for a total of 16 possibilities at this point.
3. Link these 2 relationships together:
Daniel wore the red shirt.
This clue (Dan=R) eliminates all but the following 4 orderings for the fans:
Q1=G, Dan=R, HD=B, ?=Y
?=Y, Q1=B, Dan=R, HD=G
?=Y, HD=B, Dan=R, Q1=G
HD=G, Dan=R, Q1=B, ?=Y
4. Add another clue to eliminate some of these orderings and tie in another attribute:
The green-shirted fan sat to the left of Stephen.
This clue eliminates the 2nd and 3rd orderings resulting from the previous clue.
5. Continue eliminating possibilities:
The 4 fans are Noah, the red-shirted one, the one who got a snack during the first
quarter, and the one who bought a hot dog.
From this one concludes that the ordering of the 4 fans must be:
Joseph=G, Daniel=R, Stephen=B, Noah=Y
with the 1st & 3rd fans also being Q1 & HD in some order.
Clue 3 above can now be dropped because it is a consequence of this clue and
Clue 2.
6. Now add a few clues to determine Q1 & HD and tie in the remaining attributes.
The fan who bought a snack during the 2nd quarter sat between the fans who
bought popcorn and nachos.
This forces the 1st fan to be Q1 and the 3rd to be HD.
7. One fan got pizza in the 4th quarter.
8. Stephen did not sit next to the popcorn muncher.
Obviously this is not the only set of clues which could be developed for this problem.
This just illustrates one of many possible paths which could be chosen. At this stage one
would normally study the clues looking for duplication (like Clue 3 above) and for ways
to better hide the answer. If one wants a more complex puzzle, one can now add more
fans and more attributes and continue adding clues to link the new attributes with the
previously determined structure. The complexity one can build into a logic problem is
limited only by the constructor's creativity and time.