Touch Sudoku: April 2016

Saturday, 30 April 2016

Sudoku Techniques

In this blog I will introduce techniques to solve Sudoku puzzles, without using small number notations. These techniques are easy to spot, and can be used to solve Easy to Expert level, almost any Sudoku puzzle you can find in newspapers and on websites.

Sudoku Rules and Terminologies
Technique No.1 Pointing Out - Easy Level

Technique No.2 Pointing Out - Medium Level
Technique No.3 Fitting In - Medium Level

Technique No.4 Fitting In - Hard Level
Technique No.5 Pointing Out - Hard Level

Technique No.6 Pointing Out - Expert Level
Technique No.7 Fitting In - Expert Level

Enjoy.

Sudoku Technique No.7
Fitting In - Expert Level

中文版

If we have Double Pointers, do we have Double Fitters? Absolutely yes, this post is the Expert level of Fitting In technique, Angel's Wings with Double Fitters.

See the board below, angel's two wings are at 41 and 67. Click the board to see how it works.

As you can see, number 6 in 66 can fit in two cells of box 4: 41 and 49, and number 8 can fit in two cells of row 6: 49 and 67. Cell 41, 47 and 67 form a chain that linked the two wings. Think of the two possibilities of number 6:

- If 6 goes to 41 then 61 must be 9 in row 4;
- If 6 goes to 47 then 8 goes to 67 then 61 must be 9 in box 6.

Try number 8 you have the same result, either way leads to solution 619.

If you find a chain that can link the two wings - you find the angel!

The chain can be longer, in the board below, Double Fitters of 4, 1 and 5 form a chain 89, 87, 27 and 28, linked the two wings of the angel 89 and 28, the angel is 298.

The chain can be formed by same number Double Fitters, in the board below, Double Fitter of 7 in box 7 and box 8 form a chain 76, 71, 83 and 89, linked the two wings of the angel 76 and 89, revealing the angel 6 at 85. Note here that since it's the same number chain, 71 and 83 are linked by 'seeing each other'.

Double Pointing Out and Double Fitting In can work together. In the board below, one of the wing, 85, is pointed out by Double Pointer of 7 in 76 and 43, then Double Fitter of 9 fits into 43 and 43 and 51, finally Double Fitter of 8 fits into 51 and the other wing, 59, reveal the angel 7 at 58.

There you have it, exclusively from Touch Sudoku, the Angel's Wings technique, so beautiful so powerful yet easy to spot, it will downgrade puzzles used to be considered diabolical.

Enjoy.

Sudoku Rules and Terminologies
Technique No.1 Pointing Out - Easy Level

Technique No.2 Pointing Out - Medium Level
Technique No.3 Fitting In - Medium Level

Technique No.4 Fitting In - Hard Level
Technique No.5 Pointing Out - Hard Level

Technique No.6 Pointing Out - Expert Level
Technique No.7 Fitting In - Expert Level

The puzzles in this post are from http://school.maths.uwa.edu.au/~gordon/sudokumin.php The work is licensed under a Creative Commons Attribution 2.5 License. Attribution goes to Gordon Royle and The University of Western Australia.

Sudoku Technique No.6
Pointing Out - Expert Level

中文版

So far we have been using one unit as target to do pointing out and/or fitting in, now we are going to add one dimension to it, a two-unit target!

See the board below, you can see both column 6 and row 7 are highlighted. Three empty cells and two missing numbers, 4 and 6, in the two-unit target. It seems locked: if 4 goes to 71 then 83 is 6 and 59 is 4, vice versa if you switch number 4 and 6. This situation often happen close to the end of the puzzle, make you attempt to guess.

No need of guess work in this case, the key of the lock is in box 4. There are two empty cells and two missing numbers, 6 and 8, in box 4. Number 8 won't help in this case but for number 6 we have 2 assumptions:
- If 6 goes to 44, then 71 cannot be 6, then 83 must be 6
- If 6 goes to 49, then 59 cannot be 6, then 83 must be 6
Both assumptions lead to the same solution: 836. Click the board to see it in animations.

If you could click the board again and look at the two-unit target, one of the three empty cells 83 is sharing between column 6 and row 7, the other two empty cells 71 and 59 are stretching out like 2 wings. I call it Angel's Wings. When locate Angel's Wings, we need a pointer that can point out both of the wings at the same time box 4 is just what we need, with its 44 point out 71 and 49 point out 59. I call it Double Pointer.

When you find Double Pointers that can point out both of the Angel's Wings, you find the angel!

In the board below, the angel hides in column 2 and row 6, but it needs two cell pointer 16 and 81 to reveal the Angel's Wings, head in 48, wings in 68 and 75, click the board to see it. Box 9 is the Double Pointer that points out both of the wings 68 and 75, we find the angel 6 in 48.

Box 9 also shows you the beauty of Double Pointer: it does not matter how many empty cells in the pointer unit, as long as all the empty cells can form two beams pointing to two directions.

Another example, this time the angel hides in box 2 and row 1, it takes fitter 1 and 9 in column 5 to reveal the Angel's Wings. Row 4 does the double pointing job and we find the angel 4 in 21.

Revealing Angel's Wings can be complicated, click the board below to see how it's revealed in column 4 and row 1, and click the board again to see how column 8 does its double pointing.

Finding the Double Pointer is not always easy either, click the board below to see Angel's Wings in column 1 and row 1, and click the board again to see how box 5 comes to be the Double Pointer.

And Double Pointers, relay, click the board below to see Angel's Wings in column 4 and row 7, and click the board again to see how Double Pointer row 5 points out one wing 83, relays to box 9, which relays to column 2, which points out the other wing 27, finally we find angel 6 in 81.

That's the Angel's Wings with Double Pointers, a brand new technique, but think about it, it's still Pointing Out technique, extended into two-dimension!

Sudoku Rules and Terminologies
Technique No.1 Pointing Out - Easy Level

Technique No.2 Pointing Out - Medium Level
Technique No.3 Fitting In - Medium Level

Technique No.4 Fitting In - Hard Level
Technique No.5 Pointing Out - Hard Level

Technique No.6 Pointing Out - Expert Level
Technique No.7 Fitting In - Expert Level

Sunday, 10 April 2016

Sudoku Technique No.5
Pointing Out - Hard Level

中文版

You may have guessed from the hint in my last post, the Pointing Out technique Hard level is fitting in then pointing out.

More often than not, you find less than eight number that can fit into a unit, so still more than one empty cells left, wait, we can apply Pointing Out on these empty cells! See the board below, look at box 1, there are five empty cells it, notice that 3 in 27 and 9 in 37 can fit in 15 and 16 in box 1, but that still leaves three cells 17, 18 and 19 empty, and three numbers 1, 2 and 4 missing.

Among the three missing numbers, see there are two 1s in 44 and 72? They are ready to bean their lights, click the board to see the animations. 44 points out 17 and 72 points out 18, leaving 19 the only cell left for 1, solution: 191.

That was the simplest case of fitting in then pointing out, let's see a bit more complicated example in the board below. Look at box 5, 6 and 7 can fit in 56 and 59 of box 5 because the two 6s in 41 and 82, and two 7s in 61 and 85, after their fitting in, the 3 in 22 points out cell 52, 55 and 58, leaving 53 the only cell left for 3, solution: 533.

The same deal when columns and rows are target units, from a simple case:

To a complicated one:

To a more complicated one:

The complexity does not stop there, you know, units that have fitted in cells can in turn be fitters to adjacent unit. In the board below, as 7 in 24 and 8 in 51 fit in 85 and 86 in box 8, cell 86 is also in target unit column 6, so we know 86 can only be 7 or 8, any missing number in column 6 that is other than 7 or 8, can beam light to column 6. In this case 5 in 32 points out 23, 5 in 52 points out 56 and 59, leaving 29 the only cell empty, solution: 295.

In this case box 8 is a unit fitter for column 6. And unit fitters, again, relay. I will leave more complicated examples to another post.

Now you know 5 powerful techniques, hey, they are really just 2 techniques: Pointing Out and Fitting In, applying to the target unit interactively and repeatedly. Practice them, and go solve all the Hard level puzzles.

Difficulty levels are defined differently among newspapers, websites. Hard level in Touch Sudoku is the same as the highest level (Fiendish, Expert, whatever they call it) in most newspapers, and it's the same as the highest level (called Evil) in Web Sudoku.

Yet there is a higher level in Touch Sudoku: Expert, the real expert level, including puzzles being considered diabolical. Stay tuned for more exiting techniques to solve them.

Saturday, 9 April 2016

Sudoku Technique No.4
Fitting In - Hard Level

中文版

Let's continue with Fitting In technique, in Hard level. In Fitting In Medium level, we only used cell as fitters. Why, units can be fitters too!

See the board below, in box 2 we have three empty cells 23, 26 and 29, three missing numbers 4, 6 and 9. We can see there a fitter of 4 in 32, but where is the other fitter?

Look at box 1, although there is no 9 in it, there is a 9 in 42. After pointing 42 to box 1, we know 9 in box 1 must be in 11 or 13, so box 1 can be used as a fitter that fits a 9 into box 2. Now we have two fitters 4 and 9 fit into box 2, the solution: 236. Click the board to see the animations.

Another example of box fitter fitting into column.

Again columns and rows can be unit fitters too, here is a column fitter fitting into column:

Things could get complicated:

More complicated:

Even more complicated:

I will stop here, but believe me, things could get further more complicated because, as pointers relay, fitters relay too.

So there you go, Fitting In technique at Hard level, pointing out then fitting in, which is a hint to my next blog.

Sudoku Technique No.3
Fitting In - Medium Level

中文版

Let's move to Fitting In technique, in Medium level. You may wondering where is the Fitting In Easy level, well, in Sudoku Rules and Terminology, see the examples that eight of the numbers nicely fitted in a unit? The last number goes to the last empty cell, that Easy level of Fitting In, too obvious to have a separate blog for it. But it gives the idea what Fitting In technique is: when when eight numbers can fit in a unit, the last number goes to the last empty cell.

See the board below, look at box 3, there are 3 empty cells 31, 34 and 37 and 3 missing numbers 3, 6 and 7. There is a 3 in 23 that can point out 3 from 31 but leaves two empty cells 34 and 37, there is a 7 in 11 that can point out 7 from 31 but leaves two empty cells 34 and 37, so Pointing Out technique cannot apply here.

But think from the other side, if 31 cannot be 3 then 3 must in either 34 or 37, if 31 cannot be 7 the 7 must be in either 34 or 37, so 3 and 7 can nicely fit into 34 and 37, we don't know which number in which cell but the point is, eight numbers are now fitting in box 3, leaving the last number 6 go to the last empty cell 31! Click the board to see the animations.

Another example of fitting in a box, like an orchid centerpiece.

More examples, fitting in a column:

Fitting in a row:

Fitting In technique is harder to spot than the same level of Pointing Out, especially when more than three empty cells in a unit, you need to scan three or more numbers in three adjacent units. The same solution may come from different unit depending which unit you choose to be the target. The same solution in previous board, which was four numbers fitting in row 3, could be different four numbers fitting in column 7:

Or could be other five numbers fitting in box 3:

Of course Touch Sudoku will always give you the simplest of the solutions.

With the 3 techniques so for, you can solve all the Medium level Sudoku puzzles.

Friday, 8 April 2016

Sudoku Technique No.2
Pointing Out - Medium Level

中文版

Let's continue with Pointing Out technique, in a higher level.

Look at the board below, focusing on row 4. There are six empty cells in it: 42, 43, 51, 52, 53 and 62 (Please see Sudoku Rules and Terminology on how to locate cells). Notice there are two 4s around row 4, 54 can point out 51, 52 and 53 because they are in the same box, and 32 can point out 62 because they are in the same column, but we still don't know where 4 goes since there are still two cells 42 and 43 left in row 4.

Well, turns out, not only cells can be pointers, units can be pointers too! Let's look at box 1, notice the empty cells in box 1 form a letter T. Now beam light from 32 to box 1, the three cells 11, 12, and 13 that form the upper part of the T are pointed out, leaving the two cells 15 and 18 that form lower part of the T. We don't know which one is 4 but we sure know that 4 in box 1 must be in column 2, so now box 1 can be used as a pointer, which can point out 42 in our target row 4, leaving 43 the only cell left. Click on the board, if you haven't yet, to see the animations.

Another example, box pointer pointing to column.

More examples, here is a box pointer pointing to box:

Of course columns and rows can be unit pointers too, here is an example of column-row pointing:

Another example of column-row pointing:

A special case of column-row pointing, cross pointing:

An example with a box pointing, a column-row pointing and a cross pointing:

The beauty of unit pointers is, they rely:

That's it for unit pointing, now you can use it to solve Medium level Sudoku puzzles.

Thursday, 7 April 2016

Sudoku Technique No.1
Pointing Out - Easy Level

中文版

Before I talk about the Sudoku techniques, I should let you know that, there are actually just 2 techniques: Pointing Out and Fitting In. In this post I will talk about the Pointing Out technique, in Easy level.

Look at the board below, focusing on box 1. There are six empty cells in box 1, seems clueless, but notice there is a 5 in row 1, so no other cells in row 1 can be 5, and there is another 5 in column 2, so no other cells in column 2 can be 5. Now image the two 5s can beam light, both pointing to box 1 (you can click on the board to see the animations, yes, the board is clickable!).

As you can see, the lights from the two 5s pointing to box 1 highlight the five of the six cells that cannot be 5, the only cell left out must be 5, so the solution is 195. (What is 195? see Sudoku Rules and Terminology)

The next solution is 761 in box 7, click the board to see the animations.

Now you can see how Pointing Out technique works, you focus on a target unit, image cells (with the same number) around it beaming lights to the target unit, if only one cell left out in the target, the number must go to that cell.

Of course not only a box, a column or a row can be a target unit too. See the board below.

Target unit: row 1, solution: 331

More examples, Pointing Out in a clean box:

Five pointers pointing to a row:

Six pointers pointing to a column:

That's the very basic Pointing Out technique, as simple as it is, all the Easy level puzzles you can find in newspapers and websites, can be solved using this technique alone.