Thursday, August 2, 2007

tips for solving logic problems

Logic 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. Click Bachelor Binge
Solution for a step-by-step illustrated solution of a simple logic problem. After having
worked through this example or tried others, the following more general tips may be of
help.
1. 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.
2. 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.
3. 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.
4. Watch for subtle gender clues based on names or pronouns.
5. 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.
6. 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.
7. 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.
8. 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).
9. One way to get "unstuck" is to make an assumption. If possible, find one to make
which has been narrowed down to 2 possiblilities. 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.
10. Verify your proposed solution by checking that it satisfies the introduction and all
the clues

How to contruct logic problems?

A logic problem consists of a jumble of facts and relationships from which one must
deduce an organized structure through the application of logical deduction and inference.
To construct a logic problem, one must develop a correct set of statements (clues) from
which the organized structure (answer) may be deduced. It is more difficult than it may at
first appear to develop a set of clues which uniquely determine the answer, without
revealing the answer too obviously. It also takes far longer to construct a logic problem
than it takes to solve it.
I do not know of any published material on how to construct logic problems, but I can
outline how I do it. I start with the organized structure (the answer) and work backwards
to assemble a collection of statements which uniquely determine the given structure.
Sherlock Holmes describes this type of process in a discussion with his friend Dr. Watson
in A Study in Scarlet, 1887:
Holmes: In solving a problem of this sort, the grand thing is to be able
to reason backward. That is a very useful accomplishment, and a very
easy one, but people do not practise it much. In the everyday affairs of
life it is more useful to reason forward, and so the other comes to be
neglected. There are fifty who can reason synthetically for one who can
reason analytically.
Watson: I confess that I do not quite follow you.
Holmes: I hardly expected that you would. Let me see if I can make it
clearer. Most people, if you describe a train of events to them will tell
you what the result would be. They can put those events together in
their minds, and argue from them that something will come to pass.
There are few people, however, who, if you told them a result, would
be able to evolve from their own inner consciousness what the steps
were which led up to that result. This power is what I mean when I talk
of reasoning backward, or analytically.
Below I describe the process in general and illustrate it by constructing Football Fans, the
Logic Problem of the Month for October 1997. I have deliberately chosen to illustrate the
basic construction process with an easy puzzle in order to avoid obscuring the basics with
the complexity of a hard example. (The solution to the Football Fans logic problem
appears below. One should probably work the problem first before studying the
construction process.)

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.

The cryptogram

The Cryptogram
A cryptogram, or crypt for short, is a coded message in which each letter is
replaced throughout by another letter wherever it appears. No letter may stand for
itself, and no letter may represent more than one other letter. For example, the
message Meet me here at two o’clock, or else! might be encrypted as PXXF PX AXJX
HF FIZ Z’DKZDU, ZJ XKOX!
Punctuation and the original word divisions are retained. Capitalized words are
asterisked; thus, Lily Tomlin might be encrypted as *EGEC *YQNEGM; Richard III
might be encrypted as *WSOTUWV *S*S*S. (This doesn’t apply to words that are
capitalized only because they begin a sentence.) Words that are capitalized only
because of their use are tagged with carets: ^Uncle *Remus, ^The ^Mill on the
*Floss.
Enigma cryptograms are arranged roughly in order of difficulty, from easiest to
hardest. However, what one solver finds easy, another will find hard; also, the
editor’s guesses at difficulty may not always be on target.
Tags
Unlike answers to flats (which are tagged if they don’t appear in 11C), words in
cryptograms are tagged only if they don’t appear in any of our official references
(11C, NI3, and NI2).
Rules for Cryptograms
Cryptograms in The Enigma must conform to certain rules, designed to ensure that
they are fair to the solver:
1. Each crypt must contain from 75 to 90 letters in all.
2. A letter that is used only once (such as A, H, K, S, and W in the message
“Meet me here at two o’clock or else!”) is called a singleton. You may have
no more than six singletons in a crypt.
3. Ordinarily, no more than four capitalized words should be used. (Words
capitalized only because they appear in a title are not counted.)
4. All words must appear in one of our official references or be noted as “not
MW.” “Reformed spellings” (from NI2) are not allowed.
5. The message must be a complete and coherent statement, grammatically
stated and correctly punctuated. Lists of words set off by commas are not
acceptable.
6. Each cryptogram must have a brief, appropriate title, providing some
indication of the crypt’s subject or theme, but not so directly as to give away
the answer. If you don’t supply a suitable title, the editor or crypt-checker will
write one.

Additional Guidelines for Constructors

Additional Guidelines for Constructors
One or two non-MW words in a crypt are fine, especially if they’re well-known (such
as topical references) or easily deduced from the rest of the message. Try to avoid
singletons in non-MW words. Solvers who submit solution lists won’t be penalized for
missing singletons in non-MW words if they’ve solved the rest of the cryptogram
correctly.
Try for consistency and plausibility. Unless you serve the point of the message by
doing so, don’t mix American and British spellings in the same sentence; don’t drop
one archaic word into an otherwise modern-English crypt; don’t begin Medieval
samurai inspects digital watch . . . -- unless, of course, the anachronisms are the
point.
Try to make your message interesting or amusing. A crypt that’s funny, clever,
punnish, or thought-provoking is more satisfying than a contrived string of words.
Some telegraphese is acceptable in order to avoid short, common words like and, a,
and the that can make a crypt too easy to be interesting. This clever crypt,
constructed by Arachne, uses telegraphese typically: Girl drops from blue, wears
ruby flats for trip down golden road toward leaf-hued city. Movie fans tickled pink.
Pattern words (words with repeated letters, like the Us in usual) tend to make a
cryptogram easier. Avoid them if you’re trying to make a harder crypt.
The very hardest crypts use unusual or obscure words. A typical example (by
Micropod): Hindu nastika thumps mridanga, gift from Bhutani. Kali objects,
dispatches death-bent demon. Even this is not an extreme example: occasionally a
message is so full of uncommon words that it’s just as unintelligible after solving as
it was before! The more obscure the message, the more important it is to play fair
with the solver. Be sure the message makes coherent sense. Here, for example,
nastika (an atheist) and Kali (a god’s name) are both words used in Hinduism, and a
mridanga is an Indian drum -- all appropriate to a message about a Hindu and a
Bhutani. Here, the only singletons are the L in Kali and the J in objects, well below
the maximum of six. These things can help make even the hardest cryptograms
more enjoyable and satisfying to solve. Usually, though, what the editor needs most
are neither the very easy or the very hard crypts -- these are more often in good
supply than crypts of moderate difficulty made of common words.

How to prepare for personality tests?

How to Prepare for Personality Testing Sessions?
Keep in mind...
Personality is an amazing entity. You can think. You can visualize. You can discover.
You can express. You can plan. You can create. You have unlimited hidden
potentials. But your selected options on paper are going to decide your future.
You should practice offline and online personality tests before encountering a real
session. Your practice shall not only make them familiar to you but also generate a
list of your strengths and weaknesses. You can improve them with your conscious
efforts.
However, it is much more important to learn how different personality and aptitude
tests measure expressions of your personality. What theories are working behind
them? How do they relate different jobs with different types? This knowledge shall
make it a lot easier to encounter psychometrics.

Do you have any questions?

Do You Have any Questions?
by Carole Martin
Monster Contributing Writer
Surprisingly, the most common answer to this question is "no." Not only is this the
wrong answer, but it's also a missed opportunity to find out information about the
company. It is important for you to ask questions -- not just any questions, but those
relating to the job, the company and the industry.
Consider this: Two candidates are interviewing for an inside sales position.
Henry asks, "I was wondering about benefits, and when they would become effective? Also,
what is the yearly vacation allowance? And, does the company match on the 401K plan?"
Assuming this is the first interview, it is premature to ask about benefits. "What's in it for
me?" questions can be interpreted as self-centered and a sign of your lack of interest in the
job.
The next candidate, Chris, says, "No, I think you just about covered everything I wanted to
know. I'm sure I'll have more questions if I get the job."
This is a very passive response that doesn't demonstrate interest or imagination. Once you get
the job -- if you get it -- may be too late to ask questions.
It is important to ask questions to learn about the company and the job's challenges. In some
cases, the interviewer will be listening for the types of questions you ask. The best questions
will come as a result of your listening to what is asked during the interview.
A good response to the interviewer asking, "Do you have any questions?" would be: "Yes, I
do. From what you've been asking during the interview, it sounds like you have a problem
with customer retention. Can you tell me a little more about the current situation, and what
the first challenges would be for the new person?"
This answer shows interest in what the problem is and how you could be the possible solution.
It is also an opportunity to get a sense of what will be expected.