Notes to V2V (I)

I will write the notes for two paired puzzles per thread, so the forum is not spoiled with a single thread of 3 pages.
I am considering putting all the notes in some kind of 'solution booklet', if it fullfills a need. Please let me know.

So here are the notes to the first two puzzles:

V: GT Consecutive
Normally in consecutive sudokus not so much givens are necessary, let alone in a consecutive in which you know what is the greater and what the smaller digit.
For this test I was in the mood for working with digits 1 to 9 as givens, especially since you can make a relative easy puzzle as a start of the test; besides, not many GT signs are necessary in that case.
Of course the start of the puzzle is {46} in R4C6 and R6C4. 123 and 789 can be placed in the middle block as wel as 4 in R4C6 and 6 in R6C4. Next column 7 can be filled completely: R6C7 = 4; R4C7 = 1, R89C7 = 78, 2 in R1 and 5 in R2.
No further problems or tricks in this puzzle.

V2V: Greater than X
Obviously a puzzle that a lot of people skipped, or had problems with, although some people didn’t encounter any problems at all.
Here we go:
Two of the few given digits in the grid are placed in box 8, so the puzzle is pinpointing in this direction for the first clue(s).
First the value of X:
Because of the 6 with the greater sign, X has a maximum of 5 and is not 2. It is also not 5, because of the 1 with smaller sign in row 1. The 1 in Block 8 is placed in R7C4 [Note: 1 can’t be in R8C6 because it conflicts with the smaller sign in row 1] below a GT-sign, so X is also not 3. So there are still only 1 and 4 left as possibility for X.
Try X = 1: R7C4 = 1; R8C4 = 2; 3 cannot be placed in any of the 3 remaining cells.
So: X = 4.
[Note: determining X is not 3 can be done straight away: Block 4 contains 4 GT-signs, covering 8 cells, so X is not 3.]

Let’s start solving.
R5C2 = 1
Explanation: With X being 4, 1 or 9 is not used in the four different ‘pairs’ in 3x3-Block 4.
With 1 or 9 being unused, 5 is placed in one of the ‘corner’ cells of Block 4. Since all these ‘corner’ cells are the smallest of the ‘pair’, 5 goes together with 9 and 1 is unused, placed in the middle of the block.
R1C6 = 5; R9C7 = 2; R7C4 = 1; R8C4 = 5; R8C6 = 3; R7C6 = 7
R8C2 = 4; R9C2 = 8 (Only possible combination that is left here)
R7C5 = 8 (Only possibility for 8 in row 7)
R8C5 = 2; R9C5 = 9; R2C5 = 4; R2C6 = 8
3 in row 9 in R9C89:=> 7 in Block 7 locked in R9C13.
And then a very mean naked single: R8C3 = 6.
R7C1 = 2 (Only possibility in Block 7)
5 in Block 7 in R9C13 :=> R9C13 is {57}
R8C1 = 1; R7C3 = 9
R6C2 = 6; R6C3 = 2; R6C9 = 1; R7C9 = 5; R9C9 = 3; R9C8 = 1; R8C8 = 7; R4C6 = 1
R2C3 = 1 [If 1 is placed in R3C3, there is also a ‘pair’ in R12C3, but there is no GT-sign.]
R3C2 = 5; R4C2 = 7; R4C1 = 3
And the rest shouldn’t be any difficult at all.

Notes to V2V (II)

V: Clones
I like to work with diagonal symmetry, but it is not often used in sudokus. For this clones sudoku I thougt this type of symmetry was very suitable.
The first step in solving is to realise that R6C9 = R9C7 & R7C9 = R9C6.
R7C7 = 6; R8C8 = 5; R6C8 = 2
6 is not in tetris-shape in C12 :=> R2C4 = 6 & R5C3 = 6
All 6's can be placed now
R6C2 & R2C6 = 3
Rest should go easy from here

V2V: Shaken Clones
After I constructed a Clone sudoku for the advent calender at LM Germany, I thought it would be a nice idea too to work with shapes containing the same digits, but without the restriction of fixed position of digits. By keeping the shapes inside 3x3-boxes, I had a good way keeping the number of givens to a minimum, without getting too hard.
The triomino clone contains digits 237, so R4C8 = 2; R45C9 = {37}
The 5 in the 3x3-block bottom left goes into the square clone, so R3C8 cannot be 5 :=> R3C5 = 5; R2C5 = 8; R2C4 = 4
The pentomino clone contains 4 (Block 5) and 1 (Block 1), so in column 1 the 4 goes into R4C1.
1 in row 9 must be in R9C8.
R6C9 = 1; R2C9 = 5; R8C1 = 5;
8 is not in pentomino shape:=> R9C9 = 8
4 is not in square shape:=> R8C9 = 4; R7C9 = 6; R1C9 = 9
6 is not in pentomino shape:=>R8C5 = 6; R8C6 = 1; R7C5 = 9
9 must be in pentomino shape:=> R5C4 = 9
6 must be in square shape:=> R2C8 = 6
The rest should be pretty much straight forward

Notes to V2V (III)

V: Perfect Squares
One of the two 'joke'-puzzles in the set. I thought it would be fun to include the longest possible chain of consecutive squares as a starting point (81649 in row 5).
This puzzle doesn't contain difficult steps, although you have to realise that no perfect square may be formed when there is no dot. A lot of players found solutions that contained one or more perfect squares where it wasn't allowed, so the successrating for this puzzle is not so high.
In most tests, the puzzle that is submitted the most is either the first puzzle or the one with the least points. Perfect Squares isn't one of those, but it is submitted the most, and also the most number of times with errors.

V2V: Primes
This is the other 'joke'-puzzle in the set. There are multiple examples of puzzles where a constraint doesn't appear at all in a puzzle. For that reason I created this 'primeless primes'. It wasn't easy to find a solution for the grid, but after that a nice, easy puzzle came out. It's important to realise the key role for the 3. Only 63 and 93 have a 3 as second digit without being a prime.

Notes to V2V (IV)

V: Thermometers
A lot of thermometers are built on a few given digits and long thermometer shapes. Not much have diagonal lines. Thermometers had to be one of the easier puzzles, since it is a well known variant, so I used pretty much givens and a straight forward route through the puzzle.
R46C5 = {78}
R3C3 = 8; R2C4 = 9; R7C2 = 3
R2C6 = 8; R1C7 = 9
R8C4 = 8; R9C3 = 9
R7C8 = 1; R3C5 = 5; R2C5 = 2; R8C5 = 3; R7C5 = 6; R3C8 = 2

V2V: Hot/Cold Thermometers
I had the idea for this puzzle type already for a long time, it just didn’t happen to make a few puzzles out of it. In fact the type is a blend of Increasing and Thermometers, with the bulb in the middle of the line.
There are a few specific moves/conclusions in this puzzle:
R7C5 = 9; R5C7 = 9; R2C7 = 7; R2C8 = 8;
R2C4 = 3; R2C3 = 5; R2C5 = 2;
R5C8 = 1; R4C6 = 1
9 in row 3 in Block 1; 9 in C3 in Block 1 :=> R3C3 = 9; R1C3 = 2; R3C1 = 6
R5C2 = 2; R7C2 = 5;
R3C79 = {12}; R3C8 = 3; R1C7 = 5; R6C8 = 5; R7C8 = 4
4 in Block 7 locked in R89C3 :=> R5C3 = 7/8; R4C2 = 6/7; R4C3 = 7/8; R4C4 = 8/9;
R4C2 = 6; R6C3 = 3
R7C3 = 1; R4C5 = 5
4 in R5 locked in R5C46; R8C5 = 4
Not much troubles to be expected after this stage.

Notes to V2V (V)

V: Rank
Rank was one of my favourite puzzles in Classics vs Innovatives, so I deliberately wanted to include such a puzzle in one of my own tests.
Towards the end it contains a bit of a tricky step, that can be overseen easily.
R9C8 = 7; R2C5 = 9; R3C5 = 1; R3C8 = 3; R3C4 = 6; R3C7 = 5;
R3C2 = 8; R3C3 = 2; R2C6 = 8; R4C6 = 9; R9C4 = 9; R8C5 = 8;
R9C5 = 4; R7C3 = 5; R9C6 = 5; R8C13 = {34}; R7C2 = 9; R8C9 = 9;
R5C3 = 9; R6C8 = 9; R9C9 = 6;
R1C8 + R2C7 = {46}; R2C9 = 1; R1C9 = 8; R2C3 = 7; R7C8 = 1; R8C4 =1
Towards the end, placing the 7 in Block 4 is a crucial step in getting the solution logically. By that time you know that R6C4 = either 7 or 8. That means that the 7 in block 4 can’t go in R4C2, since R4C1 must be 8 and no possibility is left for R6C4 in that case.

V2V: Rank killer
As soon as I saw the Rank sudoku for the first time, with the dotted outlined boxes, I realised that this puzzle type could be combined with killer in a beautiful way, so that variation to a variant was settled early in the puzzle creating process for this test.
R9C1 = 5; R789C2 = {123}; R9C6 = 4; R9C789 = {789}; R9C3 = 6
R9C4 = 3; R8C4 + R9C5 = {12}; R7C4 = 8; R7C56 = {56}; R5C6 = 1; R6C6 = 2;
R7C1 = 7; R7C3 = 9;
Maximum for R7C89 = 7 (3+4); maximum of R8C9 = 6; R6C8 = 9; R7C8 = 3; R7C9 = 4; R8C9 = 6
R8C2 = 3; R5C1 = 9; R3C5 = 8; R4C6 = 8; R5C2 = 5; R6C1 = 6; R5C4 = 4; R34C4 = {79};
R2C45 = {12};
1 in Block 3 locked in R13C8; R6C9 = 1; R3C6 = 3; R1C5 = 4; R1C4 = 6; R6C4 = 5;
R1C6 = 9; R2C6 = 5
R8C5 = 9; R8C6 = 7
From here no problems can be expected...

Notes to V2V (VI)

V: Even Sandwich
I like to explore the possibilities that certain types offer. In the case of Even Sandwich there are some interesting steps during the solve that make it a lot easier to proceed, one of them very early in the process. Also: by knowing there is an even digit and no sandwiched digit in the respective row or column there must be odd digits two cells away from the even digit.
R5C3 = 2; 9 in row 4 in R4C45; R4C6 = 2; R4C4 = 9; R4C57 = {46}
R35C4 = {48}
3 in C5 in R23C5; R3C6 = 1; R1C4 = 5; 5 in C6 in R56C6; R6C5 = 7; R6C4 = 3
R1C36 = {68}; R1C2 = 9; 9 in R9 only in R9C3 :=> R9C4 = 2; R9C2 = 8; R9C6 = 7
R9C78 = {16}
1 in R8 in R8C3; R8C2 = 2; 7 in Block 7 in R8C1
R5C1 = 3; R46C1 = {19}
…

V2V: Sum Sandwich
Thinking about a variation to Even Sandwich, more ideas crossed my mind. I used two of those ideas for the Advent Calender at Logic Masters Germany, namely Consecutive Sandwich and Next to Nine. I thought the third idea would be suitable for this test: Sum Sandwich. I realised quite a lot of puzzles for the test were already on the hard side, so I decided to make this one very easy. The sums of 3 and 4 provide easy starts for this puzzle.

Notes to V2V (VII)

Here are the final notes to the test puzzles.
Please feel free to respond, ask more clarifications, point me to other solving strategies (or typo's).

1~9
Playing with sums in sudokus is one of my favourite habits. I really liked the idea of a ‘floating sum’ somewhere in the row/column immediately when I saw it once at a Sudoku Cup. Deriving information from the grid, limiting the positions of 1 and 9, it’s all in here.
R2C3 = 4; R2C4 = 9
In row 8 the digit outside the sum is 2 (33 +1+9=43), so: R8C1 = 2; R8C2 = 9; R8C9 = 9
Column 2: digits in R19C2 must be {68}
Column 4: since R8C4 <>1; R9C4 = 1; R1C4 = 6
Column 3: digits outside the sum add to 8; 1 or 2 cells. Since R89C3 <>1 and 9: R1C3 = 9; R7C3 = 1; R89C3 = {35}
…

Frame 1~9
I had little reservations towards this type. I am not too fond of sudokus with complicated rules and I was a bit afraid that the large number of clues outside the grid would be confusing.
I liked the fact that on one side you give more information about each row and column, but on the other side, by giving the clues in an increasing order, you take away information as well. So all in all, I gave it a go.
Important information: no zero outside the grid means no 1 or 9 in the first and last cell, and no neighbouring 1 and 9 as well.
Wheather people found all those outside clues confusing during solving or not I can’t tell, but it’s the puzzle with the highest percentage of correct entries.
R28C5 = {19}
R6C9 = 2; R5C9 = 1; R7C9 = 9; R9C8 = 1; R9C9 = 7; R8C9 = 3; R78C8 = {25}
R9C7 = 4; R8C7 = 6; R8C8 = 5; R7C8 = 2; R9C1 = 9
9 in R4 must go in R4C4; R4C13 = {78}
…

Hi Richard, thanks for the contest, nice Sudokus as expected. My performance felt like average for me, and had no luck too with the timing, missed the Sum Sandwich by maybe 30 seconds (but thats only 30 points). I felt I needed a break after the last contest, so I had some more or less puzzle-free weeks and no preparation, otherwise I think I would have felt "overpuzzled" in the upcoming WPF Grand Prix' and of course the German Championships. Now it's time to start training again ;-)

After solving the remaining half, I'm happy I didn't do the Greater than X. Nice path and my favourite in the set, but would have cost much too much time in the contest.

How balanced do you think the puzzle types of this test were?	Perfectly balanced
What was your opinion of the distribution of easy/hard puzzles?	Just right
What did you think about the puzzle quality of the test?	Fairly Nice
How did you feel about the length / time limit for this test?	Just right
Of the puzzles you solved/attempted, how well did their point values reflect the difficulty/time spent?	Most puzzles were worth the right amount
What was your opinion of the booklet formatting and printing?	Just right

Enjoyed the test, albeit I had to do it in something of a rush. Thanks Richard!

How balanced do you think the puzzle types of this test were?	Perfectly balanced
What was your opinion of the distribution of easy/hard puzzles?	Just right
What did you think about the puzzle quality of the test?	Very nice
How did you feel about the length / time limit for this test?	Way too many puzzles (too little time)
Of the puzzles you solved/attempted, how well did their point values reflect the difficulty/time spent?	Most puzzles were worth the right amount
What was your opinion of the booklet formatting and printing?	Just right

When I say "too little time" means I need much more to solve all puzzles. However, the contests shouldn't be any longer (I even would prefer shorter, but I understand that it is than more difficult to have a balanced choice of puzzles). So the time is really ok.

How balanced do you think the puzzle types of this test were?	Fairly balanced
What was your opinion of the distribution of easy/hard puzzles?	Just right
What did you think about the puzzle quality of the test?	Very nice
How did you feel about the length / time limit for this test?	Just right
Of the puzzles you solved/attempted, how well did their point values reflect the difficulty/time spent?	Most puzzles were worth the right amount
What was your opinion of the booklet formatting and printing?	Just right

How balanced do you think the puzzle types of this test were?	Fairly balanced
What was your opinion of the distribution of easy/hard puzzles?	A bit hard
What did you think about the puzzle quality of the test?	Very nice
How did you feel about the length / time limit for this test?	Way too many puzzles (too little time)
Of the puzzles you solved/attempted, how well did their point values reflect the difficulty/time spent?	Most puzzles were worth the right amount
What was your opinion of the booklet formatting and printing?	Just right