Tutorial 2 - Working With Virtual Sets
Tutorial 2A is an example of a derived strong inference set from a broken wing pattern. A broken wing is odd length loop of 5 or more truths where 1 or more candidates called guardians prevent the loop from forming an illegal structure. If there were no guardians, the loop would be made of an odd number of strong links, which is logically impossible. Therefore at least one of the guardians must be true. The set of all guardians is therefore a strong inference set (SIS).
Tutorial 2A, Broken Wing
On startup, the currently selected puzzle file is xsudon.sud. This file contains the tutorials and a several other examples. This file is the main working file and cannot be erased.
Open the Tutorial 2A Puzzle
· Click
the right tab of the puzzle list in the toolbar............. 
· Scroll up and click on the puzzle called Tutorial 2A.
· Click
on the load puzzle icon 
to
the right.
You will now see the Tutorial 2A puzzle as shown below. The light shaded area shows the 5 truths that would form 5 strong links in a loop if not for the 4 guardians (red arrows). The task here is to make a virtual set of the 4 guardians and use it to detect the stong inference set (SIS).
Step 1, Make a Virtual Set from the 4 Guardians
· Holding down the Control Key, left click to select the 4 guardians.
· Right click one of the guardians to open the candidate menu and select [Build a Virtual Set].
· Go to the Assume Menu and select [Assume] / [Include the Virtual Set].
When the VS is included, strong inferences are indicated by red squares thus the 4 guardians form a SIS. The color blue would indicate no strong inferences.
Tutorial 2B, Replacing an AUR with a Virtual Set
Tutorial 2B will use the virtual set to replace an AUR that is part of a chain. The first step makes a virtual set to detect the strong inference. In the second step, the strong inference is replaced by the virtual set.
Open the Tutorial 2B Puzzle
· Click
the right tab of the puzzle list in the toolbar.............
· Scroll up and click on the puzzle called Tutorial 2B.
· Click
on the load puzzle icon to
the right.
You will see the Tutorial 2B puzzle shown below. The AUR in r12c47 makes a strong inference set in the 3 candidates connected to it, (48)r2c6 and (1)r2c7. The first step is to make a virtual set of these 3 candidates and use the VS to detect the SIS. In the second step, we will "apply" the virtual set to the logic and then remove the AUR, which is no longer needed when the SIS is applied to the logic.
Step 1, Make a Virtual Set from the 3 Candidates
· Holding down the Control Key, left click the 3 candidates (48)r2c6 and (1)r2c7.
· Right click one of the candidates to open the candidate menu and select [Build a Virtual Set].
· Go to the Assume Menu and select [Assume] / [Include the Virtual Set].
When the VS is included, strong inferences are indicated by red squares thus the 3 candidates form a SIS. The color blue would indicate no strong inferences.
Step 2, Apply the Virtual Set to the logic
· Select [Assume] / [No. of Truths to Apply] and set the value to 1.
· Now apply the virtual set by selecting [Assume] / [Apply the Virtual Set].
A black line connecting the 3 candidates appears indicating the active virtual set. This is easier to see in 3D. You can enter and exit 3D mode by double right clicking the mouse somewhere in the grid.
Step 3, Remove the AUR from the Logic
· Remove the 2 cell truths. Sequentially click on digit 4 and 8 in cell r1c7. Repeat for cell r2c7.
· Remove 2 box truths. Press the Alt Key and click any 2 digit 4s in box 2. Repeat for digit 8.
· Turn off the AUR by un-selecting [Assume] / [Apply AURs].
The virtual set has now replaced the strong inference set from the AUR adn the elimination remains. The grid should now look like this:
Tutorial 2C, Multi-Layer Monster Loop
Tutorial 2B is a 4 layer multi-level fish structure that forms a monster loop. This loop however has no eliminations because the layers don't make a strong inference set in its 4 vertical connecting cell links. A strong inference set requires 5 candidates in these layers. In this example, the virtual set is used to investigate the logic and fix it so that it makes eliminations.
Open the Tutorial 2C Puzzle
· Click
the right tab of the puzzle list in the toolbar.............
· Scroll up and click on the puzzle called Tutorial 2C.
· Click
on the load puzzle icon to
the right.
You will now see Tutorial 2C puzzle shown below.
Step 1, Make a Virtual Set from the 4 marked candidates.
· Holding down the Control Key, left click the 4 marked digit 5s in cells r4c48 and r5c24.
· Right click one of the candidates to open the candidate menu and select [Build a Virtual Set].
· Go to the Assume Menu and select [Assume] / [Include the Virtual Set].
When the VS is included, strong inferences are indicated by red. The candidates are blue indicating no strong inference.
Step 2, Add 5r4c6 to the Virtual Set
· Right click (5)r4c6 to open the candidate menu and select [Toggle in Virtual Set].
The virtual set turns red indicating a strong inference set.
Each layer has a strong inference set, we only used layer 5 for testing. If it takes 5 candidates to make a SIS in each layer, then there must be 5 layers vertically connected to fill the 5 SIS with 5 truths. Then the logic is rank 0 and eliminations are possible. By a stroke of luck, there is a single box truth in box b5 that can be used as a 5th layer! But first, the virtual set is no longer needed.
Step 3, Clear the Virtual Set
· Right click one of the VS candidates to open the candidate menu and select [Clear the Virtual Set].
Step 4, Add a 5th layer to the logic to cause eliminations.
· Right click 8r4c6 and select [Add/Sub Truth] / [Box] to add a box truth.
· Right click 8r4c6 again and select [Add/Sub Link] / [Cell] to link all candidates in cell r4c6.
The two eliminations r4c8<>2 and r5c2<>8 now appear