This document describes how to use Swamp Numbers on the iPod Touch and iPhone. You can use Swamp Numbers either to solve automatically generated puzzles or puzzles you enter from a book or newspaper. Swamp Numbers can generate a wide range of puzzles from those suitable for a beginner through those that might challenge even an experienced solver.

You can either solve a puzzle on your own or ask Swamp Numbers for help. When asking for help, you can either request a hint as to the next number to enter, or you can request Swamp Numbers to completely solve the puzzle. You can also use Swamp Numbers to record candidates for each cell in the puzzle. You can either enter the candidates yourself or ask Swamp Numbers to identify the candidates automatically.

Note that the standard disclaimers that apply to all software apply to Swamp Numbers, too. While we have made every effort to ensure Swamp Numbers functions properly, you use it at your own risk.

The remaining sections describe the features in detail.

- Quick Start Guide
- Overview of Controls
- Entering Puzzles
- Solving Puzzles
- Getting Help Solving Puzzles
- Correcting Errors You Make
- Snapshots
- Advanced Mode for Entering Candidates

For those who are itching to get started, using Swamp Numbers is simple.
After starting the program, click on the ** New ** button. On
the displayed screen, click on one of the numbers from 1 through 9 to
select a difficulty level. Level 1 puzzles are appropriate for beginngers.
The puzzles get progressively more difficult until level 9 which is likely
to be very difficult even for experienced solvers.

After Swamp Numbers generates a puzzle, you can proceed to solving the puzzle. Entering a number in a square consists of two steps. First, you must click on the square into which you want to insert a number. Then, you must select a number to insert into the selected square. Swamp Numbers provides a number entry area from which you may select the numbers 1 through 9. If you fill in all of the numbers correctly Swamp Numbers will display a congratulatory message indicating you have completed the puzzle.

If this brief overview is insufficient for you or if you are interested in the more advanced features of Swamp Numbers, consult the remaining sections of this document.

This section overviews the available controls. As shownnn below, the screen is divided into the following areas:

- the 9x9 grid defining the puzzle
- the usage hint area (in the following example, the usage hint area is immediately below the 9x9 grid and displays the text "Hit solve when you are done entering the puzzle.")
- the number entry area allowing you to select the numbers 1 through 9
- the buttons for selecting features (
`New`

`Solve`

`Hint`

`Clear`

`History`

If you get the program into a state that you are not sure how to exit, check the usage hint area for guidance.

Before solving a puzzle, you first need to a puzzle to solve. You can either
manually enter a puzzle from a book or newspaper or ask Swamp Numbers to automatically
generate a puzzle. Regardless of how you choose to enter a puzzle, hit the ** New **
button to access the following screen:

To ask Swamp Numbers to automatically generate a puzzle, simply select a number 1 through 9. The higher the number you select, the harder the puzzle that will be generated. The following shows a sample generated puzzle.

Note that the initial clues for the puzzle are displayed in blue. Any numbers you enter are displayed in black. The color difference is used to clarify which cells you may alter when solving a puzzle. You cannot alter any of the blue numbers since that would be cheating. Also note that once the puzzle is generated, a timer is displayed immediately above the feature selection buttons. This allows you to see how long it takes you to solve a puzzle.

Note that puzzles at levels 1 through 8 should be solvable without guessing. As you progress to higher level puzzles, you will need more expertise to solve the puzzles. Level 9 puzzles might require guessing to solve. Typically, generation of such puzzles is bad form, but Swamp Numbers provides this option for those who want more difficult puzzles. If you do not want puzzles that require guessing to solve, do not choose level 9 puzzles.

Warning: Level 9 puzzles can take up to two minutes to generate. Other difficult puzzles might take as much as 20 seconds to generate. Simpler puzzles are generated in a matter of seconds.

You can also enter puzzles from a book or magazine. For example, if you are having trouble solving a puzzle from a book and would like help, you can enter the puzzle in Swamp Numbers and use Swamp Numbers's hint features.

To manually enter a puzzle, you first need to enter Manual Entry Mode. To do this:

- Hit the
`New`

- Hit the
`Solve`

`New`

Swamp Numbers will display the following message:

This is Swamp Numbers's way of reminding you that when you have finished entering your puzzle,
you should hit the ** Solve ** key to tell Swamp Numbers that you have finished entry.
After selecting

` OK `

Note that the usage hint area serves as a reminder that once you are done entering
the puzzle you should hit the ** Solve ** key before attempting to solve the
puzzle.

To enter a number, simply click on the square where you want to put the number and then click on the number in the number entry area. For example, if we click on the square in the lower right hand corner and then click on the number 7, the display changes to the following.

Note that the currenty selected square is indicated by a yellow square. If you enter the
wrong number in a square, you can correct the error by clicking on the ** Clear **
button and then selecting

` Clear Square`

Consider the following figure demonstrating an attempt to enter a puzzle.

To inform Swamp Numbers you are done entering the puzzle, you hit the ** Solve **
button. In response, the following message is displayed:

Whenever you manually enter a puzzle, Swamp Numbers checks to see whether it is able to
solve the puzzle. Swamp Numbers should be able to solve any valid puzzle, so typically this
message is only displayed if you either made an error while entering the puzzle or the
puzzle is unsolvable. Thus, you generally should select ** Cancel ** at this point
to continue puzzle entry. In this case, the problem is that we neglected to put a 2 in the
lower right hand corner. After correcting the error and hitting the

` Solve `

Note that while Swamp Numbers has been able to solve every puzzle presented to it so far, there theoritically could be puzzles that Swamp Numbers cannot solve. If Swamp Numbers displays a warning for a puzzle that you are sure you have entered correctly, it is possible that the puzzle is valid but not solvable by Swamp Numbers. Swamp Numbers allows you to proceed to solving the puzzle in case you are confident that the puzzle is valid.

In some cases, Swamp Numbers can determine that the puzzle is impossible to solve. For example, a puzzle that has two 8's in the same row, cannot possibly be solvable. If you attempt to enter such a puzzle, Swamp Numbers will display a different warning and force you to correct the error.

As discussed previously, the numbers comprising the puzzle to be
solved are displayed in blue. The point of hitting the **
Solve ** button when you are done entering numbers is to let
Swamp Numbers "freeze" the initial puzzle to prevent you from cheating
(accidentally or intentionally) when solving the puzzle.

Once you have either generated or entered a puzzle, you are ready to start solving the puzzle. To solve, repeatedly enter numbers in the squares such that each row, column, and 3x3 box contains the numbers 1 through 9.

To enter a number, simply touch the square in which you want to
put a number, and then select the number from the number entry
area. If you make an error, you can either hit the **
Clear ** button to make the square empty again or overwrite the
value you entered by selecting a different value from the number entry area.

For now, just use the ** Clear Square ** option accesible by hitting
the

` Clear `

` Clear Errors `

` Clear Past Error `

Also note that a short cut for clearing a square is to re-enter the number that is already in the square. For example, if a square currently contains the number 3, then you can clear the square by selecting the square and then selecting 3 from the number entry area.

When you correctly solve the puzzle, the numbers will change to green and a congratulatory message will be displayed. The following illustrates Swamp Numbers indicating you have solved the puzzle. The timer will stop once you solve the puzzle allowing you to tell how long it took.

If the congratulatory message is not displayed and the timer continues running after you fill in the last square, you have made an error in the puzzle. See the next section if you need help locating your error.

Note that if you are distracted by other matters while solving a puzzle and would like to pause the timer, you can simply exit Swamp Numbers by returning to the Home screen. When you restart Swamp Numbers, it will resume with the same puzzle and the same timer value.

You can ask Swamp Numbers to solve the puzzle for you at any time by simply clicking on
the ** Solve ** button. This takes all of the enjoyment out of solving the puzzle,
but is of use if you simply want to know the solution. For example, suppose that you have
chosen to work a puzzle from a newspaper but did it with pencil and paper without using
Swamp Numbers. Rather than waiting until the next day to see if the published solution matches
your solution, you could enter the puzzle and let Swamp Numbers provide you a solution against
which to check your answer.

Swamp Numbers always prompts you to ensure you really want it to
solve the puzzle to protect against you accidentally hitting
the ** Solve ** button. If you accidentally confirm that you
want the puzzle solved, but really wanted to go back to solving the
puzzle yourself, you can get back to the puzzle by hitting the

` History `

` Back`

` Back `

Swamp Numbers provides a number of options for obtaining help in solving a puzzle.
By default, all of the hint mechanisms are turned off allowing you to solve puzzles
on your own. To enable the hint mechanisms, hit the ** Hint ** button. Swamp
Numbers will prompt you as follows:

Note that if you accidentally hit the ** Hint ** button,
you can select

` Cancel`

` Cancel`

Beginners might want to select ** Show Hints**. This switches Swamp Numbers into
hint mode. Swamp Numbers will remain in Hint Mode until you hit the

` Hint `

` Show Errors `

` Show Neither`

The blue square indicates a square that Swamp Numbers is indicating you should be able to figure out. The pink squares indicate squares that Swamp Numbers thinks will be helpful for you to determine the number that belongs in the blue square. In this example, Swamp Numbers is indicating that the only place the number 1 can go in the 4th row is in the blue square. All of the other squares in the 4th row either already have a number or are in a column that the pink squares show already contains a 1.

Note that the yellow square, as usual, indicates the currently selected square. So, rather than simply selecting 1 from the number entry area, you first need to select the blue square to make it the currently selected square and then select 1 from the number entry area.

While Hint Mode can be helpful for beginngers, once you get the hang of solving puzzles, you will probably only want to use Hint Mode when you are stuck. To do so, simply solve the puzzle as you normally would and enter Hint Mode only when you are stuck. Once you use the hint to get unstuck, you can exit Hint Mode to continue solving the puzzle on your own. You can move into and out of Hint Mode whenever you want.

Hint Mode should be of help any time you are stuck on a puzzle below level 9. As the puzzles get more complicated, the hints become more cryptic. For example, the following is an example from a level 8 puzzle.

A lot of thought is required to figure out whether the blue square should contain a 4 or a 6. Internally, Swamp Numbers notices that the only options for the number 6 in row 3 are in columns 4 and 5. This means that the 6 in the 3x3 box at the top middle right must be in the third row. So, the square in the 1st row 6th column is either a 1 or a 4. Then, the only square in the 6th column that can contain a 6 is the one in row 7. So, the 6 goes in the 7th row 6th column and the 4 goes in the blue square. The puzzle is easily solved from this point.

Basically, the hint is indicating that once Swamp Numbers realized where the 6 went, it could figure out where the 4 went by looking at the pink squares. One could argue that it would have been better for Swamp Numbers to give a hint for how to figure out where the 6 goes, but providing the best hint in all cases is difficult. Fortunately, the simpler the puzzle, the more clear the hints. Since less experienced solvers are likely to work simpler puzzles, the cryptic hints are only an issue for hard puzzles that are likely being solved by experienced solvers that can interpret the hints.

The main drawback of Hint Mode is that it can remove much of the fun of solving puzzles
by simplifying the process too much. If you choose ** Show Errors ** instead of

` Show Hints`

In this example, the red 7 near the bottom right corner is
incorrect. If you want to try solving puzzles on your own but be
warned when you make accidental mistakes, then this Error Notification
mode is a good mode. As long as you remain in this mode, any errors
will be displayed in red. To exit this mode, you need to hit the ** Hint **
button and then select

` Show Neither`

Note that because some users are expected to want to leave Error Notification Mode on at all times, this mode persists across puzzles. In other words, once you turn on Error Notification Mode, it will remain on for all of the puzzles you solve until you explicitly turn it off.

Note that the Hint Mode described previously automatically turns on Error Notification Mode. In other words, whenever you turn on Hint Mode, you are also turning on Eror Notification Mode. Hint Mode will be automatically disabled whenever you move to a new puzzle, but Error Notification Mode will remain on.

Finally, note that the background changes from red to black whenever you have Error Notification Mode enabled. This provides a quick visual cue as to whether you are in Error Notification Mode.

A common approach people use for solving more advanced puzzles is to write little
numbers called * candidates * into each square. Swamp Numbers provides support
in case you want to enter such candidates in each square. In this section, we discuss
how to ask Swamp Numbers to fill in the candidate values for you. Section
Advanced Mode describes how you can enter candidate values
yourself.

To request Swamp Numbers to fill in candidate values for you, simply select
** Fill Candidates ** from the list of choices presented when you hit the

` Hint `

In this example, we created a new puzzle and then immediately asked Swamp Numbers to fill in candidates. All of the squares that contain a single black number are squares for which Swamp Numbers noticed there was only a single candidate. For example, consider the square in the lower left hand corner. When attempting to determine the candidates for the square, Swamp Numbers sees that all of the number except for 3 are impossible for the square. Rather than putting a small 3 in the square by itself to indicate a single candidate, Swamp Numbers puts a large 3 in the square to indicate that square is solved. When solving simpler puzzles, choosing Fill Candidates can fill in many numbers in this manner.

To further understand the operation of Fill Candidates, consider the square containing the numbers 2 and 5 in the 7th row and 5th column. The square directly below this square contains the number 5. Clearly, the 5 is not a viable candidate for the square with candidates 2 and 5. Why did Swamp Numbers not realize the only real candidate was 2?

The reason is that Swamp Numbers fills in the candidates square-by-square from the upper left to the lower right. At the time the 7th row was being processed, Swamp Numbers had not yet determined the location of the 5 in the 8th row. While the Fill Candidates feature could have been implemented to repeatedly recompute candidates until no further reductions can be made, this could in some cases cause the whole puzzle to be solved. Since having Swamp Numbers automatically solve the puzzle for you would not be that instructive, we have Fill Candidates stop after a single pass over the board. Note, however, that nothing prevents you from asking Swamp Numbers to Fill Candidates again. If we do that continuing from the previous diagram, the result is as follows.

At this point, consider the upper left hand 3x3 box. The 4 and 8 must go in the first column, so the square containing candidates 4, 7, and 8 must contain a 7. This is an example of how candidates can help solve puzzles. Of course, in this particular puzzle, you could also have seen that the 7 goes in the second box of the second row by seeing that we already have 7's in the 1st and 5th columns and all of the other squares are already filled.

You can correct mistakes you make while solving a puzzle by hitting the ** Clear **
button. Swamp Numbers provides the following options:

` Cancel `

` Clear `

` Cancel `

` Clear Square `

` Clear Errors `

Here, we filled in all of the squares, did not receive the congratulatory messages
indicating the puzzle was solved, entered Error Mode, and realized we had made a
number of errors. At this point, we might want to see if we could get the correct solution
if we removed all of the errors. To do so, we choose ** Clear Errors ** and
get the following.

At this point, we could continue solving the puzzle until we reached the correct
solution. Some might feel that this is cheating since it is possible that some of
the correct numbers were just correct by chance. They should consider using the
** Clear Past Error** feature. If we used this instead of

` Clear Errors `

The subtle difference between the two is illustrated by looking at
the 7th row 2nd column. When we used ** Clear Errors **,
this square contained a 4. When we use

```
Clear Past
Error
```

Which of the two options you use is your choice. Generally, ** Clear Past Error **
will erase more numbers and thus leave you more work to do. However, your reward for doing
the extra work is knowing that you solved the puzzle without relying on numbers you
entered after your first error that happened to be correct through chance.

Of course, another option is to clear all of the numbers you entered and return to
the original puzzle. You can do this by hitting the ** History ** button and
choosing

` Restart`

Swamp Numbers provides a limited ability for you to save snapshots of the current grid. Generally, you should not need this feature and we recommend this feature only for advanced users.

You access snapshots by hitting the ** History ** button. Doing so provides the
following choices:

As usual, the ** Cancel ** option simply closes the selection window without
changing the current grid or mode.

The ** Snapshot ** option saves the current grid to a snapshot. You can save
up to 8 of these snapshots. An example of when you might want to use a snapshot is if
you know that a square contains 1 of 2 numbers but are not sure which value it contains.
Then, you might simply want to try the first number and see if you can solve the puzzle.
The problem is that you might find that the puzzle is unsolvable and then need to go back
to try the second number. If you create a snapshot before trying the first number, you can
then use the

` Back `

If while trying the first number, you got to a point where you again needed to guess,
you could create a second snapshot. After entering more numbers, you could decide to go
back to the second snapshot using the ** Back ** option. If you wanted to
go back to the first snapshot, you would use the

` Back `

` Forward `

The main reason we do not recommend the use of snapshots is that sometimes they
can cause more problems than they solve. For example, suppose you create a snapshot,
fill in a lot more numbers, and then accidentally use the ** Back ** option.
At that point, all of the work you did after creating the snapshot is lost.

In most cases, we recommend using Hint Mode instead of snapshots. If you get to the point where you think you need to guess, rather than creating a snapshot and guessing, try using Hint Mode to get you unstuck without guessing. The primary reason we have provided the snapshot feature is for users selecting level 9 puzzles that might require guessing to solve.

Note that the ** Restart ** option erases all of the numbers that you
have entered while trying to solve the puzzle. In other words, this reverts the puzzle
back to its original state. You can use this if you discover you have made an error in
the puzzle and want to start over. For other options, see the
Correcting Errors section.

For users that want to enter little numbers (candidates) in each
square as part of their solving strategy, Swamp Numbers allows entry of
small numbers in each square that indicate all of the numbers that
could go in that square. As described previously, the ** Fill
Candidates ** option accessible via the

` Hint `

If you either want to enter candidate numbers yourself or want to modify
candidate numbers created using the ** Fill Candidates ** option,
you need to use Advanced Mode. To use Advanced Mode, you simply double click
on the square for which you want to enter candidates. The following shows the
use of Advanced Mode to enter candidates for the square in the upper right hand corner.

When in Advanced Mode, the blue square indicates the square for which you are entering candidates. The yellow 3x3 square shows you the candidates currently thought possible for the square. In this case, all numbers from 1 through 9 are shown as candidates. By looking at the last column, we know that the only possible candidates are 2 and 8. We can toggle whether a number is in the candidate set by clicking on the yellow square corresponding to its position. In this case, we click on all of the numbers except the 2 and the 8 to obtain the following.

Note how the blue square is updated to match the yellow square. If you accidentally remove a candidate that you did not intend to remove, you can add it back to the set by clicking on its spot in the yellow box. For example, if we click on the square at the upper left hand corner of the yellow box, then we would add 1 back into the candidate set. When you are done entering candidate numbers, simply click on the blue square to exit Advanced Mode. You can enter and exit Advanced Mode as many times as you would like. For example, you might enter a candidate set for a square, do a bunch more work on other squares, and then realize you can remove another number from the candidate set for the first square. At that point, you can simply double click on the first square to edit its candidate set.

Note that all of the buttons are disabled while you are in Advanced Mode. You must click on the blue square to exit Advanced Mode before using the buttons.