The following project
uses the game of Guess Your Card. This is a game in which each
playerdraws (without looking) three cards. Each card has a number
between 1 and 9 on it. The playersthen place their cards on their heads
so that everyone but themselves can see the cards.The object of the game
is to guess what cards you have. The first person to do this
correctly,wins.During the play, each player, in turn, draws a question
at random from a stack of questions.The player then answers the question
based on the cards that they see (not their own cards, whichthey cannot
Andy has the cards 6 6 7
Belle has the cards 3 6 7
Carol has the cards 1 1 9
Dan has the cards 3 4 8
Andy draws the question card, “How many 7s do you
see?” He answers, “one,” because hecannot see the 7 on his own head; he
sees only the 7 on Belle’s head.Next Belle draws the question card, “Of
the four even numbers, how many different even numbersdo you see? She
answers “three,” because she sees the 4, 6, and 8 on Andy and Dan’s
head. Fromthis, Dan can conclude he has two even cards, since he can
only see a 6 and Belle sees two more.
The Project’s Situation
You are playing Guess Your Card with three other players. Here is what you see:
Andy has the cards 1 3 7
Belle has the cards 3 4 7
Carol has the cards 4 6 8
Andy draws the question card, “Do you see two or more players whose cards sum to the samevalue?”
He answers, “Yes.”Next Belle draws the question card, “Of the five odd numbers, how many different odd numbersdo you see?
She answers “All of them.”Andy suddenly speaks up.
”I know what I have,” he says. ”I have a one, a three, and a seven.”The
QuestionWhat cards do you have?
In answering this question, you must write a neat and professional report. You need to briefly
summarize the salient facts of the problem, explain your strategy for solving the problem, explain
why your strategy will work, execute your strategy, show your mathematical working, draw conclusions
from your working, and finally present your answer with a brief summery of why it is your
Remember, your strategy is to use more than logic. What kind of logic will you use?
Writing assignments are to be typed solutions. The best way to envision how these papers
are to be constructed is to imagine that you have been hired to answer the questions given in the
assignments. When problem analysts submit their reports to their clients, they do more than simply
answer the question. The document is broken into four parts; in order:
The Problem: This is a statement of the problem that you have been asked to solve. It is
stated in a single, simple sentence. Any necessary and significant details should follow. Think of
this as being the question you have ultimately been hired to answer. Be sure to use your own words.
Remember that your audience is aware of what question they hired you to answer, however, it most
likely has been a fair amount of time and they are busy people. You want to be clear, concise,
include everything important, but don’t waste the readers time.
The Approach: What strategy will you use to solve this problem? This is tougher to convey in
a single, simple sentence, and sometimes even a single paragraph. However, you can almost always
begin with a statement saying the method that you used. Follow this with an overview of how you
put the facts together with the technique to get an answer.
This is not a section of mathematical calculations. No calculations are seen here at all. In fact,
this section must be written in future tense, as though you have not already done this work. You
are writing as though you are explaining a proposed method of solving the problem, not from the
standpoint of someone who has already done the work.
Remember, this section is about how you will solve the problem. It cannot seem as though
you have already drawn a conclusion. It should not read like you have already done the work.
Otherwise, you could be accused of bias; if the analyst profits from a particular answer, then they
will choose a method that will lead to this answer. To avoid this perception, you need to maintain
a tone and style of detachment. You do not care which answer you receive for the question, only
what the answer is, whatever it is. To help ensure this tone, you need to include the different
conditions under which you will draw your different possible conclusions. Ultimately, all these
projects involving calculating some value(s) and then choosing a course of action based on this.
Explain what range of values of your possible solution(s) correspond with which courses of action.
Conclusion: Here you start by stating the recommended course of action. You follow this with
a summary of the reasons for your recommendation. This section is the most important section.
You must be sure you are conveying everything needed without boring the reader with extraneous
information. Your reasoning needs to tie back into the explanation you gave in The Approach
regarding how you would choose the course of action.
Solution Details: Only now do you include the mathematics. You must include not just the
calculations, but also a brief explanation of each calculation.
You should also consider the following questions in writing any report.
1. Neatness and professionalism of presentation:
• Is your text legible, on white paper with black ink?
• Are your pages stapled, without frilly edges, of regular size (81
2 × 11), and uncrumpled?
• Have you used sentences and paragraphs appropriately?
• Is your text reasonably free of typos and spelling mistakes?
• Does your presentation include an opening statement describing what you intend to
present and a conclusion wrapping up the presentation?
2. Appropriateness and explanation of problem solving strategy: 10 points
• If preformed correctly, will your strategy solve the problem?
• Is it clear to the reader why your steps will solve the problem?
• Are the steps of your strategy in a logical order?
• Are there any redundant or unnecessary steps?
3. Implementation of strategy:
• Did you follow the strategy you outlined?
• Did you preform the steps of your strategy correctly?
4. Use of appropriate mathematical notation and language:
• Are you using mathematical language as opposed to common, less precise language?
• Are you using mathematical language according to its definition as opposed to a less
• Are you using the symbols of mathematics correctly?
5. Presentation of the results presented in the context of the question:
• Is the question you are asked, answered?
• Is it clear from your presentation (both in the opening and closing) what the question
you are answering is?
• Does your answer include a brief summery of why you decided on this answer?