Kakuro Tool

A Tailor-Made App

User reference manual

-*-*-*- DRAFT February 12, 2020 -*-*-*-

Introduction

The Kakuro Tool is intended as a trusted companion for anyone solving Kakuro puzzles on paper with pencil and eraser.

When solving Kakuros, you often need to work out exactly which digit combinations are possible for a given sum considering a number of extra constranints. While it is possible to generate these list by hand, it is a tedious, mechanical task and not one that adds to the fun of solving the puzzle.

The centre of the app is the "Kakurolator", which is a combination calculator accepting the sum and field count as primary inputs:

Consider a sum of 17 in 4 fields entered into the Kakurolator

resulting in 9 possible combinations. While solving a Kakuro there are two schools of thinking of combinations: "Bottom-up" and "Top-down" as illustrated above. Many people find it natural to see combinations "Bottom-up", i.e. starting with small digits and ending in the largest digits. However, some find it more effective to view combinations starting with the highest values because the bigger digits tend to limit the choices faster. With Kakuro Tool you can select which direction to use at any time through settings. For the remainder of this manual, we stick to the "Bottom up" direction as it seems to be the most common view especially for beginners but urge users to try out the "Reverse digit order" option as it soon becomes addictive.

Now consider this fragment of a Kakukro, which has a sum of 17 in 4 fields:

To solve the 17-sum, we first consider the column with sum 30 in 4 fields. The only solution is "6 7 8 9" but the crossing rows result in some constraints, which are marked by writing the set of possible digits in each field.

The 30-sum must have a "6" and the only possible position is as the first digit of the our 17-sum. Thus we can write the "6" and update the Kakurolator with the constraint that "6" is a "required" digit, leaving only three possible combinations.

Further checking on the remaining fields of the 17-sum reveal that none of them can contain 8: 7 is the unique sum of "1 2 4", 16 is the unique sum of "1 3", 4 is the unique sum of "1 3".

We can therefore enter "8" as a "rejected" digit in the Kakurolator reducing the number of combinations to only two.

To narrow down further, we look at the the available digits for the remaining three fields in the two combinations: "1 2 3 4 5 7". We cannot reject "2" and "4" because the are both possible in the second field of the 17-sum but only in that field. If we look at the two possible combinations separately, we see that we must either have both "2" and "4" (in "2 4 5 6") or none of them (in "1 3 6 7"). As we only have one field accepting "2" or "4", we can rule out using the combination "2 4 5 6". To remember the result of this analysis we can strike out the impossible combination:

We are now left with only one possible digit combination for this particular sum and only need to see how these digits can fit with the crossing sums. This is the result

Kakuro puzzles are sometimes referred to as a cross-sum puzzle, stressing the main source of constraints to the digit combinations comes from the crossing of several sums. Consequently, it is very useful to be able to see several sets of possible combinations at the same time. For that reason it has been important to make each combination calculator as small as possible to fit more information into a single screen of the device and further place the Kakurolator in a scrolling screen. The maximum allowed configuration is 12 by 12 allowing for 144 simultaneous sets of combinations.

Main screen

The Kakuro Tool is focused on a single main screen, which is a 2D scrollable area containing many Kakuro caclulators, the so called "Kakurolators", organized in a number of columns holding rows of Kakurolators, which all operate independently of each other.

All the marked elements of the main screen are described below:

• Title
  The name of the app.
• Countdown
  Optional countdown timer, which can be used to limit the time spent solving Kakuros as they can become quite addictive and time consuming. When the time of your choosing runs out, a dialog box asks whether you want to continue or close the app.
• Kakurolator
  The centerpiece of this app is the Kakurolator. A Kakurolator represents a single row or column in a Kakuro puzzle and is able to calculate all the possible digit combinations for that particular row or column while taking known digits and other constraints into account.
• Sum
  The first input field of the Kakurolator, Σ, is for the sum (sometimes called the "clue") of the row or column.
• Count
  The second input field of the Kakurolator, #, is for the number of fields comprising the given sum (or "clue").
• Required
  The third input field of the Kakurolator, +, holds a list of digits that must be included in the given sum.
• Rejected
  The fourth input field of the Kakurolator, -, holds a list of digits that must not be included in the given sum.
• Keypad
  Input values for the four input fields of the Kakurolator are entered through the default numeric keypad of the current Android device. Consequently, the layout and size of the keypad varies from device to device depending on the manufacturer of the device and alternative keyboard apps installed by the user.
• Options menu
  There are a number of options and settings available to the user. These are detailed in the sections Options menu and Settings below.
• Strike out
  If one or more of the possible combinations listed can be ruled out, it is possible to mark them with a "strike out" to further limit the possibilities to be considered in the course of solving the Kakuro.
• List of results
  The bottom part of each Kakurolator contains the list of results or a text indicating that there is either not enough information available to calculate results (Enter sum&count) or that the given input has no possible combinations (No combinations).
• Next input field
  The "Next" button on the keypad advances the cursor to the next input field, cycling back to the first field from the last field making continuous adjustments easy.

Context menus

Context menus are available by long-pressing in the main screen (where all the Kakurolators are). There are two different menus; one pertaining to a specific Kakurolator; one pertaining to an entire column.

Kakurolator context menu

A long press on any of the Kakurolators will open the context menu named "Combination Menu" as shown below.

The menu offers a choice between 4 actions. The first three pertain to the specific Kakurolator that was pressed while the final option affects the entire column. The options are:

• Reset
  Clears all input fields of the Kakurolator making it ready for a new set of data.
• Insert
  Inserts a new, empty Kakurolator above the selected one.
• Remove
  Removes the selected Kakurolator. Repeatedly removing Kakurolators makes it possible to empty an entire column of Kakurolators, should you wish to do so. The column can be populated with new Kakurolators through the Column context menu described below.
• Reset Column
  Resets all the Kakurolators of the selected column to their empty state..

Column context menu

A long press in an empty part of a Kakurolator column will open the context menu named "Column Menu" as shown below.

This menu offers two choices, as follows:

• Add Combination
  Adds a new, empty Kakurolator at the bottom of the column.
• Reset Column
  Resets all the Kakurolators of the selected column to their empty state..

Options menu

The three vertical dots to the right in the title bar opens the "options menu", which comes in one of two versions depending on whether the countdown timer is active or not:

The available options are:

• Reset all
  Clears all input fields of all the Kakurolators. This is mainly useful, when an entire Kakuro is solved and you want to start working an a new one.
• Start countdown
  This is only visible, if the countdown is not active. When pressed, the countdown will be initialized to the current timeout setting (see Timeout in minutes).
• Cancel countdown
  Stops and removes the countdown timer. The Kakuro Tool continues to function without any set time limit.
• Settings
  Opens the main settings window, which allows for a number of choices to be made. All settings are described in full in the section Settings below.

Settings

The main settings screen is opened from the "Settings" entry in the Options menu see Options menu above. The main settings screen provides access to all settings and provides some general information about the app developer and publisher as well as the specific app version, which is important, if an error needs to be reported.

The available settings are:

• Keep screen on
  Clears all input fields of all the Kakurolators. This is mainly useful, when an entire Kakuro is solved and you want to start working an a new one.
• Layout
  Opens the "sub-settings screen" pertaining to the layout and operation of the Kakurolators in the main screen. Layout settings below.
• Countdown timer
  Opens the "sub-settings screen" pertaining to the countdown timer. All details of the screen are described in section Countdown timer settings below.
• About
  This is not actually a setting but general as well as specific information on the origin of this app and the specific version running now, which is important, if a request for support or a suggestion is to be made concerning the app.

Layout settings

Three things can be changed. However, the control over Rows and Columns is not available in the Demo version. The available settings are:

• Reverse digit order
  It feels very natural to most of us to count things from 1 and up and thus to examine possible combinations starting from the smallest digits. However, some Kakuro solvers tend to examine the larger digits first because a bigger digit will consume a bigger portion of the sum to be made and thus put a stronger constraint on the remaining set of digits. To support this way of thinking, this option will reverse all result listings and show the possible combinations starting with the largest digit. Try it and see which you prefer.
• Rows (1 to 12)
  Offers control over the number of Kakurolators entered into each column. While using the app, the number of Kakurolators can be changed by adding and removing them individually in the columns. This setting takes effect immediately, hence the number of Kakurolators per row is forced to be the selected count, adding and removing elements as required. Any results shown in removed Kakurolators are lost. Not available to demo users.
• Columns (1 to 12)
  Offers control over the number of columns available in the scrollable area. This setting takes effect immediatly, hence if the number of columns is reduced any results shown in the removed columns are lost. Not available to demo users.

Countdown timer settings

The countdown timer can be customized through these settings.

• Timeout in minutes (1 to 999)
  The amount of time that the count shall run can be set freely between 1 and 999 minutes. At every start or restart of the countdown, it will start from this many minutes.
• Autostart
  If this setting is on, the countdown is automatically started when the app is started.

When the countdown expires, the following dialog is presented:

The Time expired dialog offers three choices:

• CONTINUE
  Continue working in the app without a countdown timer.
• RESTART TIMER
  Start a new Timeout in minutes countdown period and then continue working in the app.
• EXIT
  Terminate the app immediately, thus losing all current results.