Tutorial 5, Uniqueness

Xsudo computes uniqueness in a general way that does not depend on known uniqueness methods. It should therefore find all uniqueness but this is difficult to test. Xsudo has two ways of working with uniqueness

Small AURs. (Using 2 to 9 candidates) The user can enter between 2 and 9 candidates to form multiple simple AURs. Each AUR is assumed to have 8 candidates and the AURs can overlap. In this mode only two candidates are used to mark each AUR but they must be different digits on opposite corners of the AUR. It is possible to mark two overlapping AURs by marking only 3 candidates and thus mark large numbers of AURS.

Large AURs. (Using 10+ candidates) Xsudo allows a single large AUR that can be almost any size from 10 candidates up. In this mode, all of the potential candidates must be marked. This is done to allow for "hidden" uniqueness that may not use all candidates in a cell.

Activation

AURs can be added anytime. They are only activated by selecting [Assumptions] / [Apply AURs] in the main menu. AURs are not valid for puzzles with more than 1 solution and will have no effect. Xsudo allows AURs in sample logic (a logic drawing without a puzzle) which of course has no true solutions. A puzzle with no solutions is considered as sample logic.

The following brief tutorials explain how to enter each type of AUR logic.

A. Simple 8 candidate rectangles (Tutorial 5A)

AUR candidates are marked by using [Toggle AUR Corner] in the candidate popup menu. This function toggles AUR candidates on and off. In the simple mode, any two candidates of different digits on opposite corners of a UR define an AUR. Combinations of candidates can thus identify a large numbers of overlapping AURs. Xsudo automatically recognizes all possible URs that can be made from the selected candidates.

Open the Tutorial 5A Puzzle

· Open the dropdown puzzle list in the toolbar by cliscking the tab located on the right.

· Scroll to find and select the puzzle Tutorial 5A, Simple AURs

· Click on the load puzzle icon to the right.

Tutorial 5A contains logic that has a potential AUR. Initially, the UR is not marked and there are no eliminations. The potential UR is aur(25)r49c78.

Mark the AUR corners and activate AURs

· Select (2)r4c7 then right click to bring up the candidate popup menu.

· Repeat for candidate (5)r9c8 to complete the UR.

· Activate the AUR by selecting [Assumptions] / [Apply AURs] in the top menubar

Two eliminations and one assignment will appear, along with a light rectangular area designating the UR.

Change the graphics style (optional)

· Select [LogicView] / [Show AURs as Black Cand.] to show the UR are black candidates.

B. Large unique logic with 10++ candidates (Tutorial 5B)

In large mode, 10, 12, 16 or more candidates can be marked to make one unique logic structure of (almost) any shape. This method can be used for BUGs, BUG-Lites, and MUGs. In large mode, all candidates that make the unique logic must be manually selected. Xsudo will find any unique logic that would lead to multiple solutions, i.e., supports the uniqueness assumption. Only one large AUR is allowed in this mode.

Open the Tutorial 5B Puzzle

· Open the dropdown puzzle list by clicking on the tab located on the right.

· Scroll to find and select the puzzle Tutorial 5B, A complex AUR (theory)

· Click on the load puzzle icon to the right.

This tutorial is a sample logic drawing without a full puzzle however, the logic is the same as if it were in a puzzle.

Mark the AUR corners and activate AURs

· The 6 AUR corners have been already marked for convenience

· Activate the AUR by selecting [Assumptions] / [Apply AURs] in the top menubar.

The AUR eliminates 8r1c2, which leads to the assignment of 6r1c2.