Mystery Master

Introduction

Welcome to the Mystery Master program, the most powerful and interactive logic puzzle solver you can find! This manual will explain what a logic puzzle is, and how the Mystery Master can help you solve them. If you are interested in obtaining the Mystery Master program, please visit our website at www.mysterymaster.com page.

The Mystery Master program is a Multiple Document Interface (MDI) application, because it can display several different windows at once within the main window. These windows are also known as forms. A form that must be closed before you can do anything else is called a modal window (also called a tool window or dialog). Forms that do not need to be closed are modeless windows, because you can interact with one or more of them at the same time.

To display the various pieces of information that comprises a logic puzzle, the following forms are used.

• Properties. This form displays the puzzle's name, title, and level of difficulty.
• Objects. This form displays the objects in the puzzle, organized by object type.
• Verbs. This form displays the verbs and marks used in the puzzle.
• Links. This form displays the links used to describe the relationships of the objects in the puzzle.
• Facts. This form displays the facts in the puzzle.
• Rules. This form displays the rules in the puzzle.

To help you solve a logic puzzle, the Mystery Master program employs the following puzzle-solving tools.

• Options. This form allows you to set all solving options.
• Console. This form displays the current status of the puzzle.
• Chart. This form displays the current solution to the puzzle.
• Grid. This form displays the marks for any combination of two object types.
• Marks. This form displays all marks in chronological order.

Besides forms, the Mystery Master program also has a menu, a toolbar, and a status bar. Next, we will describe what a logic puzzle is.

What Is A Logic Puzzle?

A logic puzzle is a story that usually has an introduction, followed by a list of clues. Some logic puzzles will also include clues in the introduction as well, so make sure you read the entire puzzle carefully. These clues explain the relationships between the objects in the story. Based on these relationships, you solve a logic puzzle by filling in a grid with X's and O's. An X means that two objects cannot be together, whereas an O means that the two objects are together. The Mystery Master program uses the generic term "with" to mean that two objects are together. A logic puzzle is considered solved when you can fill in the grid without contradicting any of the clues in the puzzle.

Throughout the manual, we will use the one-star logic puzzle "Spy Girls", which you can find on the puzzles page. You may want to display or print this puzzle before continuing.

Examine All Clues

The first "listed" clue in our puzzle is "Sylvia is ranked higher than Agent Adams, but is not the highest." While most logic puzzles itemize all the clues for you, there may also be clues and/or objects in the introduction. For example, the introduction says (to paraphrase): "The all-female spy agency consists of Jane and four other agents, one of whom is Agent Brookes." Therefore, the first clue is actually "Jane is not Agent Brookes." All the clues in this puzzle are:

1. Jane is not Agent Brookes.
1. Sylvia is ranked higher than Agent Adams, but is not the highest.
2. Hillary's rank is higher than Agent Darling, but not as high as Agent Brookes.
3. Amanda is ranked higher than either Kate or Hillary, but is not the highest.
4. Agent Adams is ranked higher than Agent Miller, but is ranked lower than Agent Cooper.
5. Agent Miller is not ranked the lowest.

Determine Objects and Relationships

As we mentioned before, clues explain the relationships between the objects in the story. Objects are nouns like "Sylvia" and "Agent Adams", and relationships are phrases like "is ranked higher than". After identifying all the objects and relationships in the puzzle, we need to organize the objects by object type. Object type is like a group or category that each object goes under. The object types, and object for each type, are given below.

1. Agents: 1, 2, 3, 4, 5
2. First Names: Jane, Sylvia, Hillary, Amanda, Kate
3. Last Names: Brookes, Adams, Darling, Miller, Cooper

The relationships that we can easily see in this puzzle are "is ranked higher than" and "is ranked lower than". The relationships that are a little harder to specify are in phrases like "Jane is not Agent Brookes" and "Sylvia... is not the highest". We will show how you can easily find relationships in the next section.

Gather The Facts

If you carefully examine clue 1, you'll see two distinct statements:

• Sylvia is ranked higher than Agent Adams.
• Sylvia is not the highest ranked agent.

These statements are called facts. A fact defines a relationship between exactly two objects. Relationships are broken down into two parts: verbs and links. The verbs for this puzzle are "is" and "is not". The links for this puzzle are "with" and "ranked higher than". Sometimes the link between two objects in a fact is implied. For example, in the clue "Jane is not Agent Brookes.", the link is implied to be "with". Examining all the clues in our logic puzzle reveals the following facts:

1. Jane is not Agent Brookes.
2. Sylvia is ranked higher than Agent Adams.
3. Sylvia is not Agent 1.
4. Hillary is ranked higher than Agent Darling.
5. Agent Brookes is ranked higher than Hillary.
6. Amanda is ranked higher than Kate.
7. Amanda is ranked higher than Hillary.
8. Amanda is not Agent 1.
9. Agent Adams is ranked higher than Agent Miller.
10. Agent Cooper is ranked higher than Agent Adams.
11. Agent Miller is not Agent 5.

It should be noted that the following modifications were made to the facts:

1. "highest" was changed to "Agent 1", and "lowest" was changed to "Agent 5". This just refers to our objects.
2. For the tenth fact, the order of the two objects was reversed and the link was changed from "ranked lower than" to "ranked higher than". This change was made in order to be efficient with our links.

After carefully examining all of the clues, we organized the objects in the puzzle by object type, and converted all the clues to facts. And we saw that by changing the order of the objects in a fact, we needed to specify just two links. One last note - if this puzzle was more difficult, not all of the clues could have been converted to facts. If a clue cannot be expressed as a fact, then it must be defined as a rule. Rules are conditional statements, such as "If Sylvia's last name is Brookes, then Hillary is not Agent 5." Now that we know (almost) everything we need to know about a logic puzzle, let's shift our focus to the Mystery Master program.

New Logic Puzzle

Note: The main purpose of the Mystery Master program is to solve logic puzzles. It is not intended to create logic puzzles. If you (a) will use existing puzzle modules, or (b) have no desire to program, then you should probably skip this section. Also, I will not be discussing programming in this manual.

If you want to create your own puzzle module, you will need (1) membership in the Mystery Master Agency (via a donation) to access source code, and (2) the desire to write code in the C# programming language. The amount of programming you are required to know is related to how difficult the logic puzzle is. To give you an idea of how much programming is involved, the source code for all puzzle modules is available to members of the Mystery Master Agency.

For example, here is the source code (SpyGirls.cs) for the logic puzzle "SpyGirls".

To create new puzzle modules, I use the Microsoft Visual Studio .Net IDE (Integrated Development Environment), which costs a lot of money. Fortunately, you can download Microsoft's Visual C# 2008 Express Edition, which is free! You can use either editor to create and/or modify a puzzle module.

Open Logic Puzzle

Note: If you do not have the Mystery Master program already installed on your computer, please go to the setup page. If you do have it, please run the program now.

Before you can solve a logic puzzle, you first need to tell the Mystery Master program what puzzle you want to solve. You do this by loading a specific logic puzzle file into the program. In case you're wondering, a logic puzzle file (called a puzzle module) is really a Dynamic Link Library ("dll") file. But don't worry, you don't need to be a programmer to use a puzzle module; you only need to know how to use a computer mouse and keyboard.

To specify what logic puzzle to solve, select File|Open from the menu, or click on the icon from the toolbar. This will display the Open Puzzle File dialog box, where you select the puzzle you want. You make your selection by either double-clicking on the file of your choice, or highlight the file you want and press the Open button. We will next describe the various forms that display information about a logic puzzle.

The Properties Form

The properties of a logic puzzle consists of information that is important to know, but is not really required to solve the puzzle. An example of the Properties dialog form is given below for the logic puzzle "Spy Girls".

Here is a brief description of each property:

• Name - The name of the logic puzzle file (without the ".dll" extension).
• Title - The full title of the logic puzzle.
• Stars - The rank of the puzzle from one star (very easy) to five stars (very difficult).

The Objects Form

Objects are the things (nouns) given in the clues of the puzzle. Objects are organized by object type, where object type is like a group or category that each object goes under. The number of objects for each type will always be the same! Most puzzles provide all of the objects in the text of the puzzle, though some force you to look at the chart and/or grid to get the objects not mentioned in the puzzle. A few puzzles (usually the very difficult ones) will force you to calculate the name (or value) for some of the objects!

Objects are displayed in the Objects dialog form, where the object types are the column headers and the objects for each type are in the appropriate column. Objects are used in defining facts and rules, and are displayed in the Chart and Grid forms. An example of the Objects form is given below for the logic puzzle "Spy Girls". As you can see in this example, the object types are "Agent", "First Name", and "Last Name" and the number of objects per type is 5. Notice that the names of the object types are singular, not plural.

The Verbs Form

Verbs (along with links) are used to create the relationships in a puzzle. The verb names are phrases like "is not" and "is", and have a corresponding character like 'X' and 'O'. Verb names are used in the Facts form, and are also used to generate various messages displayed while the Mystery Master program is solving a puzzle. Verb characters are what you enter into the Grid form. There are three types of verbs:

• Negative - Indicates that two objects cannot be together ('X')
• Positive - Indicates that two objects are together ('O')
• Possible - Indicates that two objects may be together (a blank)

An example of the Verbs dialog form is shown below for the logic puzzle "Spy Girls".

The Links Form

Links describe the relationships between two objects in a puzzle, and are used to create facts and rules. For the logic puzzle "Spy Girls", only two links are necessary - "with" and "ranked higher than". You should note that we eliminated the link "ranked lower than" by using "ranked higher than, and switching the two objects. Sometimes the link between two objects in a fact is implied. For example, one clue states: "Jane is not Agent Brookes.". For this clue, the link is implied to be "with". In fact, the first link, "with", is always required for every logic puzzle!

An example of the Links dialog form is given below for the logic puzzle "Spy Girls".

The Facts Form

Facts are derived from the clues in the puzzle, and have the following syntax: "Object1 Verb Link Object2." You can see that a fact consists of a relationship between exactly two objects. You will find that for most logic puzzles, a clue will usually contain one or more facts. The Facts form shown below displays all of the facts for the logic puzzle "Spy Girls".

If a fact is checked, it means the fact is to be examined by the program. Once a fact has been fully examined by the program, it will uncheck it. You may also manually check and uncheck facts. It should be noted that all the clues for this logic puzzle can be given as facts. If any part of a clue cannot be given by a fact, then it must be defined as a rule.

The Rules Form

Rules are required when a clue cannot be specified by one or more facts. Since the logic puzzle "Spy Girls" does not have any rules, you can skip this section. But if you are interested, here is an example of the Rules form for the logic puzzle "Student Logic". When a rule is checked, it means that the program will examine that rule while solving the puzzle. This puzzle is unusual because it has two rules, and no facts!

The Console Form

The Console form displays information about a puzzle, and is updated while a puzzle is being solved. It also has buttons to solve, pause, and quit solving a puzzle. When you press the Solve button, the program will begin to solve the puzzle. While the puzzle is being solved, the Solve button will act as a pause/resume button. The various pause buttons control where the program will pause while a puzzle is being solved, and you toggle them to turn them on or off. There is a pause button for each Mark, Placement, Fact, Rule, Level change, and Guess made. The pause buttons can also be controlled via the Pause tab in the Options form. Pressing the Quit button tells the program to abort solving the puzzle. One of the most important controls on this form is the message box, which displays how the program is solving a puzzle. The numbers that are shown in the Console form are:

• Current number and total number of marks
• Current number and total number of placements
• Current number and total number of facts
• Current number and total number of rules
• Current level number
• Current number of guesses made (assumptions)

Below is an example of the Console form after the first mark has been entered for the logic puzzle "Spy Girls".

The Chart Form

The Chart form displays the current solution to a puzzle. You cannot enter anything into this form, but you can control what object type is displayed in the first column. While the program is solving a puzzle, if two objects are known to be with each other (an O is entered into the grid), then those two objects will appear on the same row in the chart. If the Chart Order option is on, the chart will automatically adjust to show both objects associated with a positive (O) mark. For example, if an O was entered for Jane and Darling, then the First Name column will automatically become the first column. Turning off this option essentially "freezes" the order of the object types already in the chart. But you can still manually select what column goes first by clicking on the column header. For example, clicking on the Last Name column header will display the last names in the first column. Below is an example of how the chart looks when the logic puzzle "Spy Girls" is first loaded into the Mystery Master program.

The Grid Form

The grid displays all the unique combinations of object types in a grid format. Either you or the program would enter a mark at the intersection of two objects, where a mark is either X (false) or O (true). No mark (which is really a space) means "maybe" (unknown). For example, the fact "Jane is not Agent Brookes." would prompt you to enter X for Jane and Brookes. Only when two objects have a O in the grid will they display on the same row in the chart.

Since a grid can became very unwieldly when there are many object types, the Grid form displays the marks entered for one combination of object types at a time. Use the Prior and Next buttons to display each combination of object types. The first grid (Grid 1) displays the objects for object types 1 and 2. Grid 2 displays the objects for object types 1 and 3, and Grid 3 displays the objects for object types 2 and 3. Because the puzzle "Spy Girls" only has three object types (Agent, First Name, and Last Name), there is no Grid 4 for this puzzle. Given below are examples of all three grids after the first twenty marks have been entered.

Each button performs the following task:

• Undo - Undo the last mark entered
• Delete - Delete the current mark
• Prior - Display the prior object type combination
• Next - Display the next object type combination

Question: How many unique grids are required if there are four object types? Five? Try to think of a formula where n is the number of object types in a puzzle.

The Marks Form

The Marks dialog displays all the marks that were entered into the Grid form. For each mark, there is a row in this form that gives the explanation for why the mark was entered. Below is an example of this form after the first twenty marks were entered for the logic puzzle "Spy Girls". For our members, here are all of the marks for this puzzle.

Question: What is the formula for finding the number of marks for a particular puzzle? For the number of placements (positive marks)?

The Options Form

The Options form is a dialog that allows you to specify the solving options you want. To display this form, either select Solve|Options from the menu, or click on the icon from the toolbar. The options you select will only go into effect after you press the Accept button. There are six tabs on this form: Assistance, Pauses, Modules, Levels, Laws, and Preferences.

The Assistance tab allows you to select the level of assistance you desire. The default is Custom - Enable specific Modules, Levels, and Laws. If you have not changed any other options, this is the same as the Novice setting. At the Novice setting, the Mystery Master program will solve the puzzle for you.

The Pauses tab allows you to select when the Mystery Master program should pause. The default is to pause only when the program has found a solution. Pausing can also be set via the Console form.

The Modules tab tells the Mystery Master program whether it should use facts and rules. For example, the program should use all facts and rules at the Novice setting (because the program is solving the puzzle), but the program should not use all facts and rules at the Expert setting (because you are solving the puzzle).

The Levels tab allows you turn on or off the levels used by the Mystery Master program while it is solving a puzzle. In general, all levels should be on if the program is solving the puzzle, and all levels should be off if you are solving the puzzle. Levels are discussed further in the next section.

The Laws tab allows you to turn on or off the laws used by the Mystery Master program while it is solving a puzzle. In general, all laws should be on if the program is solving the puzzle, and all laws should be off if you are solving the puzzle. Laws are discussed further in the next section.

The Preferences tab allows you to set additional preferences. If the Chart Order is turned on, whenever two objects are found to be together, the first of the two objects will show up in the first column. If Fast Mode is turned on, all forms will only be updated when a solution is found.

Levels and Laws

My favorite "laws" are those written by Isaac Asimov in his book of short stories, "I, Robot". These laws are called The Three Laws of Robotics, and they govern the behavior of a robot. Well, the Mystery Master has its own set of laws (and levels), which govern how the program solves a logic puzzle. The Levels tab on the Options form list the five levels the Mystery Master program uses to enter a mark. If all the levels are turned off (unchecked), then the program cannot solve a puzzle. It will wait until you enter a mark. The five levels are given below.

1. Examine all facts where the link is "with".
2. Examine all facts where the link is not "with".
3. Invoke a "process of elimination." Can one object be with another object?
4. Examine two facts at a time where both facts have one object in common to see if the other objects in those facts can be together.
5. Guess (make an assumption). Assume that one object is with another object.

The six laws of the Mystery Master program are invoked whenever a mark is entered, either by you or the program. The first five laws basically do the common tasks that must be done when you manually solve a puzzle. The sixth law looks at the facts with an emphasis on the mark just entered. Remember that a mark involves two objects, where the mark "X" denotes the two objects are not together, and the mark "O" denotes the two objects are together. These six laws, also found on the Laws tab of the Options form, are listed below.

1. If one object of type 1 is with another object of type 2, then object 1 cannot be with another object of type 2.
2. If only one object of type 2 is available to be with an object of type 1, then object 1 must be with object 2.
3. If object 1 is with object 2, then all objects [not] with object 2 are [not] with object 1.
4. If object 1 is not with object2, then object 1 is not with any objects that are with object 2.
5. If object 1 and object 2 have no objects of type 3 in common, then object 1 cannot be with object 2.
6. For an object that was just placed, examine all facts that refer to that object.

If you truly want to understand how these levels and laws work, you should run the Mystery Master program with all of the pausing turned on. That way you can "step" through the solving process of a particular puzzle. Another way to do this is to look at the Marks form while a puzzle is being solved.

Solve a Logic Puzzle

Using the Mystery Master program to solve a logic puzzle is very simple. Usually, you will perform the following steps for each logic puzzle you want to solve.

1. Select a Logic Puzzle using the File|Open menu.
2. Select the options you want either using the Options form and/or the Console form.
3. Display/resize one or more of the solving forms: Chart, Grid, and Marks.
4. Solve the puzzle by selecting Solve|Start from the menu, click the button on the toolbar, or click the Solve button on the Console form.

Depending on how difficult the puzzle is, the Mystery Master program will find a solution within a second (for easy puzzles) to several seconds (for difficult puzzles). The solution to the logic puzzle will appear in the Chart form. For our members, here is the solution to our logic puzzle.

If you manually solved a puzzle using paper and pencil, there are two useful tools you have probably employed, the Chart and the Grid. The chart is a table that displays objects by object type, with each type in its own column. If you enter two objects in the same row, this means that the two objects are together. For example, seeing Agent 1 and Jane in the same row of the chart means "Agent 1 is (with) Jane". The chart for this puzzle (along with every puzzle on the Mystery Master website) is included with the puzzle.

The grid displays all the unique combinations of object types in a grid format. You enter a mark at each intersection of two objects, where the mark is either an X (false) or O (true). No mark (which is really a space) means "maybe" (unknown). Only when two objects have a O in the grid will they display on the same row in the chart. For our members, here is the grid for "Spy Girls".

You solve a logic puzzle by examining each fact, and entering the appropriate marks into the grid. For example, fact one states "Jane is not Agent Brookes", you would enter an X for Jane and Brookes. Since fact one does not provide any more information than this, you are done with this fact and may move on to fact two. Since fact two states: "Sylvia is ranked higher than Agent Adams.", you would enter an X for Sylvia and Adams. Why? Because if Sylvia is ranked higher than Agent Adams, then this means Sylvia cannot be Agent Adams. What else does this fact tell us? It also implies that Sylvia cannot be the lowest ranked agent, and Agent Adams cannot be the highest ranked agent!

For more difficult puzzles, you may need to make an assumption ("guess") in order to solve the puzzle. If in the course of solving the puzzle you encounter a contradiction, you will need to undo your marks all the way back to your incorrect assumption, and try another assumption. But, if you can fill the entire grid without encountering a contradiction, then you have solved the puzzle! Fortunately, this puzzle is simple enough that you do not need to make assumptions.

To manually solve a puzzle using the Mystery Master program, you only need to change the options found in the Options form. If you want absolutely no help at all, select Expert - All assistance is off. from the Assistance tab on the Options form. Now, if you ask the Mystery Master program to solve the puzzle, nothing will happen! You enter marks directly into one or more of the Grid forms. If you make a mistake, use the Undo button or the Delete button found on the grid form. The Undo button will undo the last mark you entered, and the Delete button will delete the current mark.

There are several things you can do if you need help solving a puzzle on your own. You can have the program solve the puzzle, pausing on each mark until you get past the point where you are stuck. You can look at the section titled Levels and Laws and see what order the Mystery Master program looks at the facts. You can even let the program find a solution, then look at the Marks form to see how the program solved the puzzle. You'll find that the Mystery Master is here to help!

How to Solve "Spy Girls"

I will describe how to use the Mystery Master program to manually solve the "Spy Girls" logic puzzle. You should run the program and open the puzzle module SpyGirls.dll. Next, make sure you can see each of the following forms: Facts, Console, Chart, and Grid. You should notice that each of the facts have a checkmark next to them. As we examine each fact, we will uncheck it when we have completely examined that fact. To make sure that the program does not help us, select Solve from the menu, then Options, then from the Assistance tab select Expert - All assistance is off. Then press the Accept button. Now we are ready to examine the facts and enter our marks into the grid.

First, we will examine facts that clearly state that one object is or is not with another object. The facts where the relationship is with are facts 1, 3, 8, and 11. If the fact tells us that the two objects are not together, then we enter an X into the grid for the two objects. If the fact tells us that the two objects are together, then we enter an O into the grid for the two objects. To enter a mark in the Grid form, you will need to press the Prior and Next buttons on the form to display the correct combination of object types. For this puzzle, the three combinations are: Grid 1: Agent \ First Name, Grid 2: Agent \ Last Name, and Grid 3: First Name \ Last Name.

Fact 1 states "Jane is not Agent Brookes."
Fact 3 states "Sylvia is not Agent 1."
Fact 8 states "Amanda is not Agent 1."
Fact 11 states "Agent Miller is not Agent 5."
Based on these facts, we will enter the following marks.

1. Fact 1 has been examined. Enter 'X' for Jane and Brookes.
2. Fact 3 has been examined. Enter 'X' for 1 and Sylvia
3. Fact 8 has been examined. Enter 'X' for 1 and Amanda.
4. Fact 11 has been examined. Enter 'X' for 5 and Miller.

You may have noticed that every time you entered a mark, the Console form confirmed this. For these four facts, you can uncheck them in the Facts form. We have manually done what the Mystery Master program would do at level one. For level two, we will now examine the remaining seven facts, facts 2, 4, 5, 6, 7, 9, and 10. You should notice that you will almost always enter more than one mark for each of these facts.

Fact 2 states "Sylvia is ranked higher than Agent Adams." The first question you should ask yourself is "Can Sylvia be Agent Adams?" Since the answer is no, this will be one mark. The next question is "Can Sylvia have the lowest rank?" Again, the answer is no, since there will always be at least one agent lower than Sylvia (Adams in this case). The third question is the opposite of the second question, "Can Agent Adams have the highest rank?" The answer is no, because at least one agent (Sylvia) will always be higher. Please enter the following marks for fact 2.

5. Examining fact 2, enter 'X' for Sylvia and Adams.
6. Examining fact 2, enter 'X' for 5 and Sylvia.
7. Examining fact 2, enter 'X' for 1 and Adams.
8. Examining fact 2, enter 'X' for 2 and Adams.

Why can't Agent Adams be ranked second? It is because we already know that Sylvia is not Agent 1 (fact 3)! Since the highest Sylvia can be is Agent 2, the best Adams can be is Agent 3 in order to satisfy fact 2. Therefore, Adams cannot be Agent 2.

Fact 4 states "Hillary is ranked higher than Agent Darling." This means that Hillary is not Agent Darling, Hillary is not the lowest agent, and Agent Darling is not the highest agent. Please enter the following marks for fact 4.

9. Examining fact 4, enter 'X' for Hillary and Darling.
10. Examining fact 4, enter 'X' for 5 and Hillary.
11. Examining fact 4, enter 'X' for 1 and Darling.

Fact 5 states "Agent Brookes is ranked higher than Hillary." This means that Hillary is not Agent Brookes, Brookes is not the lowest agent (Agent 5), and Hillary is not the highest agent (Agent 1). Also because we know that Hillary is not Agent 5 (from fact 4), the lowest Hillary can be is Agent 4. Because Agent Brookes is higher than Hillary, Brookes cannot be Agent 4. Please enter the following marks for fact 5.

12. Examining fact 5, enter 'X' for Hillary and Brookes.
13. Examining fact 5, enter 'X' for 4 and Brookes.
14. Examining fact 5, enter 'X' for 5 and Brookes.
15. Examining fact 5, enter 'X' for 1 and Hillary.

Fact 6 states "Amanda is ranked higher than Kate." To state the obvious, because Amanda and Kate have the same object type (First Name) it is already implied that Amanda is not Kate. But what can be derived from this fact is that Amanda is not the lowest agent (Agent 5), and Kate is not the highest agent (Agent 1). So please enter the following marks for fact 6.

16. Examining fact 6, enter 'X' for 5 and Amanda.
17. Examining fact 6, enter 'X' for 1 and Kate.

This is where we will deviate from how the Mystery Master program solves this puzzle. While the program would start invoking laws to enter additional marks, we will finish up the remaining facts.

Fact 7 states "Amanda is ranked higher than Hillary." Since Hillary is not Agent 5 (fact 4), Amanda cannot be Agent 4. Since Amanda cannot be Agent 1 (fact 8), Hillary cannot be Agent 2. Please enter the following marks for fact 7.

18. Examining fact 7, enter 'X' for 4 and Amanda.
19. Examining fact 7, enter 'X' for 2 and Hillary.

Fact 9 states "Agent Adams is ranked higher than Agent Miller." This means that Adams is not the lowest agent (Agent 5) and Miller is not the highest agent (Agent 1). Since Agent Miller is not Agent 5 (fact 11), Agent Adams cannot be Agent 4. Since Agent Adams is not agent 1 or 2 (fact 2), Agent Miller is not Agent 2 or 3. Enter the following marks for fact 9.

20. Examining fact 9, enter 'X' for 5 and Adams.
21. Examining fact 9, enter 'X' for 1 and Miller.
22. Examining fact 9, enter 'X' for 4 and Adams.
23. Examining fact 9, enter 'X' for 2 and Miller.
24. Examining fact 9, enter 'X' for 3 and Miller.

Fact 10 states "Agent Cooper is ranked higher than Agent Adams." Looking at grid 2, we can clearly see what rank Agent Adams holds, but we will hold off entering that elusive O mark for a little longer. Since Adams must be Agent 3, Agent Cooper must be either Agent 1 or 2. So please enter the following marks for fact 10.

25. Examining fact 10, enter 'X' for 3 and Cooper.
26. Examining fact 10, enter 'X' for 4 and Cooper.
27. Examining fact 10, enter 'X' for 5 and Cooper.

We have gone as far as we can examining the facts. We now need to apply additional logic, or what the Mystery Master program calls Laws. Laws are discussed in the section Levels and Laws. One law (Law 2) can be applied by simply looking at the grids. If all cells except one in a row or column have an X, then the remaining cell must have an O. Examining Grid 1, we can clearly see that Jane must be Agent 1. Another law (Law 1) can also be applied by looking at the grids. If a cell has an O, then the remaining empty cells in the same row and the same column must have an X. We will now enter the following marks.

28. Applying Law 2, enter 'O' for 1 and Jane.
29. Applying Law 1, enter 'X' for 2 and Jane.
30. Applying Law 1, enter 'X' for 3 and Jane.
31. Applying Law 1, enter 'X' for 4 and Jane.
32. Applying Law 1, enter 'X' for 5 and Jane.

Did you notice that Jane appeared in the First Name column of the Chart form when you entered an O for 1 and Jane? Continuing, we can see that Kate must be Agent 5. Please enter the following marks.

33. Applying Law 2, enter 'O' for 5 and Kate.
34. Applying Law 1, enter 'X' for 2 and Kate.
35. Applying Law 1, enter 'X' for 3 and Kate.
36. Applying Law 1, enter 'X' for 4 and Kate.

Examining Grid 2, we can see that Adams must be Agent 3, so enter the following marks.

37. Applying Law 2, enter 'O' for 3 and Adams.
38. Applying Law 1, enter 'X' for 3 and Brookes.
39. Applying Law 1, enter 'X' for 3 and Darling.

Examining Grid 2, we can see that Darling must be Agent 5, so enter the following marks.

39. Applying Law 2, enter 'O' for 5 and Darling.
40. Applying Law 1, enter 'X' for 2 and Darling.
41. Applying Law 1, enter 'X' for 4 and Darling.

Examining Grid 2, we can see that Miller must be Agent 4, so enter the following mark.

42. Applying Law 2, enter 'O' for 4 and Miller.

Examining Grid 3 does not help us, so we need to apply some more logic. Another law (Law 3) states that if object 1 is with object 2, then (1) all objects with object 2 are with object 1, and (2) all objects not with object 2 are not with object 1. Here's how it works. We know that Jane is Agent 1. We also know that Jane is not Agent Brookes. Therefore, Brookes is not Agent 1. Examining Grid 2, we can then conclude that Brookes is Agent 2, and ultimately, Cooper is Agent 1. Enter the following marks.

43. Applying Law 3, enter 'X' for 1 and Brookes.
44. Applying Law 2, enter 'O' for 2 and Brookes.
45. Applying Law 1, enter 'X' for 2 and Cooper.
46. Applying Law 2, enter 'O' for 1 and Cooper.

Applying the knowlege Law 3 gives us, we can return to Grid 3 and easily see that Jane's last name is Cooper, and Kate's last name is Darling - or we can just look at the Chart!

47. Applying Law 3, enter 'O' for Jane and Cooper.
48. Applying Law 1, enter 'X' for Jane and Adams.
49. Applying Law 1, enter 'X' for Jane and Darling.
50. Applying Law 1, enter 'X' for Jane and Miller.
51. Applying Law 1, enter 'X' for Jane and Miller.
52. Applying Law 1, enter 'X' for Sylvia and Cooper.
53. Applying Law 1, enter 'X' for Hillary and Cooper.
54. Applying Law 1, enter 'X' for Amanda and Cooper.
55. Applying Law 1, enter 'X' for Kate and Cooper.
56. Applying Law 3, enter 'O' for Kate and Darling.
57. Applying Law 1, enter 'X' for Kate and Brookes.
58. Applying Law 1, enter 'X' for Kate and Adams.
59. Applying Law 1, enter 'X' for Kate and Miller.

To complete grids 1 and 3, we can return to our facts to see if we can fill in the missing pieces. Re-examining fact 2, since Sylvia is higher than Agent Adams, and Adams is Agent 3, then Sylvia must be Agent 2. Ultimately, Grid 1 reveals Hillary is Agent 4, and Amanda is Agent 3.

60. Examining fact 2, enter 'O' for 2 and Sylvia.
61. Applying Law 1, enter 'X' for 3 and Sylvia.
62. Applying Law 1, enter 'X' for 4 and Sylvia.
63. Applying Law 1, enter 'X' for 2 and Amanda.
64. Applying Law 2, enter 'O' for 4 and Hillary.
65. Applying Law 1, enter 'X' for 3 and Hillary.
66. Applying Law 2, enter 'O' for 3 and Amanda.

Complete Grid 3 with the following marks.

67. Applying Law 3, enter 'O' for Sylvia and Brooks.
68. Applying Law 1, enter 'X' for Amanda and Brooks.
69. Applying Law 1, enter 'X' for Sylvia and Darling.
70. Applying Law 1, enter 'X' for Sylvia and Miller.
71. Applying Law 3, enter 'O' for Hillary and Miller.
72. Applying Law 1, enter 'X' for Hillary and Adams.
73. Applying Law 3, enter 'O' for Amanda and Adams.
74. Applying Law 1, enter 'X' for Amanda and Darling.
75. Applying Law 1, enter 'X' for Amanda and Miller.

We have solved the puzzle! I should point out that there was more than one way to solve this logic puzzle. I tried to solve it in the most direct manner, but feel free to apply whatever method works for you. I hope you find a greater appreciation for logic puzzles, along with the time and effort spent to create the Mystery Master program, and this manual.

Conclusion

Congratulations - you've made it to the end of the manual! Hopefully, you have found this manual to be very informative. If you have any questions or comments, please send an email to webmaster@mysterymaster.com. This manual, along with the Mystery Master website and program, represents an investment of thousands of hours. You can show your appreciation by making a donation. Thank you.

When you are ready to tackle the other logic puzzles we have, please consider joining the Mystery Master Agency!

Glossary

Assumption: see guess.

Chart: A visual tool for solving logic puzzles. The chart shows the objects that are placed together (have a 'O' in the grid).

Clue: Clues describe the relationships between objects. An example of a clue is: "Sylvia is ranked higher than Agent Adams, but is not the highest." In the Mystery Master program, clues are broken down into facts and rules.

Contradiction: A mark that violates a fact or rule. The mark must then be undone.

Fact: Facts are used to solve a puzzle. A fact is defined as: Object1 Verb Link Object2. An example of a fact is: "Sylvia is ranked higher than Agent Adams."

Grid: A visual tool for solving logic puzzles. The grid shows the objects of one type as row headers, and the objects of another type as column headers. The program and/or the user can enter a mark at the intersection of two objects.

Guess: If a puzzle cannot be solved by the facts alone, then the user must make an assumption by entering a mark, and see whether it is true or leads to a contradiction.

Law: Logic used by the Mystery Master program after a mark is entered.

Level: Logic used by the Mystery Master program to enter a mark.

Link: Links are used, along with verbs, to describe the relationship between two objects in a fact. Examples of links are "with" and "ranked higher than".

Mark: A Verb character ('X' or 'O') that is entered into the grid. The program keeps track of who entered the mark, the two objects associated with the mark, and other information.

Object: The things (nouns) that appear in a logic puzzle. Examples of objects are "Sylvia" and "Agent 1".

Object Type: The category or group for the objects in the puzzle. Examples of object types are "First Name" and "Agent".

Placement: When a positive mark ('O)' is entered into the grid for two objects. These two objects will also show up in the chart.

Relationship: Relationships are given for two objects in a fact, and may be used in programming rules. Examples of relationships are "is with" and "is not ranked higher than".

Rule: Rules are conditional statements, and must be programmed into a puzzle. An example of a rule is: "The winners of the English and French contests were wrong.."

Solution: When all objects are placed with an object from each object type, the puzzle is said to be solved. The chart then displays the solution.

Verb: Verbs are used in creating facts. The default verbs are "is not", "is", and "may be", and the corresponding verb marks are 'X', 'O', and ' ' (a space).