Wednesday, May 27, 2009

Elements of Good Puzzles

PUZZLE ANALYSIS:

This is my list of 8 things a puzzle will have or should have.


INNATE/REQUIRED ELEMENTS OF A PUZZLE:

You will find these characteristics in all puzzles. Without them, it can't really be a puzzle.


1. An Underlying system of rules.
Rules any means used by the puzzler to constrain the valid solutions to a puzzle. They define the allowable processes and/or values that can be applied/used.
Most commonly a puzzle will use one or more of the following underlying systems: Math, Logic, Language, Geometry, Spatial Relations.


2. A Real World Mask.
A mask is a way to create a more approachable interface to the abstract concepts involved in many puzzles. It allows for the audience to more easily understand what is being asked and how the "rules" work. It is much better to refer to a deck of cards, because most people know what's in a deck of cards. It would be more tedious and confusing to refer to a set of 52 items that have a unique combination of 2 integers from the sets of values (1-4) and (1-13).
Similarly, everyone can picture a security guard chasing around a pond to catch a swimming duck.
Without the real world mask, a puzzle isn't really a puzzle. Its just a problem.


3. A Process.
Puzzles can be divided into 2 categories.
Type A: Find an Answer.
Type B: Find a Process.

The DeCAPitated movies puzzle was Type A. We were asked for a specific answer: The name of the movie.
The card-trick puzzle was Type B. An event was described and we were asked to determine the process being used to get those results.

In both cases, a process is key to solving the riddle.

In the DeCAPitated movie puzzles, you only need the "answer", but the real challenge is finding the best process to find that "answer". You could randomly insert letters into every variable and then cycle through every single word in that huge list. But that would be woefully slow.
It is much better to use intelligent guessing based on what you know about the most common arrangements of letters, and to start from the most likely word segments.

In the card-trick puzzle finding a process is the actual goal. We use our knowledge, logic, and reasoning to reverse engineer the trick.

Some other good examples of process based puzzling...
The old standby... how to get a fox, chicken, and bag of grain across a river in a boat that can only hold one of the three.
Another good example.. how to find a couterfeit coin that could be lighter or heavier in a pool of 12 coins with only 3 weighings on a balance.



ATTRIBUTES OF GOOD PUZZLES.

The real reward of any good puzzle is that warm and fuzzy feeling of being smart. To deliver that feeling a puzzle must reward intelligence. It should ideally provide the path to the answer or at least a short cut that allows you to reduce the number of guesses in half or better. Here are some of the characteristics of a good puzzle.


4. Hidden Relationships and/or Equivalencies.

A hidden relationship or equivalency is often the key to finding a puzzle's solution.
For the mirrored numbers puzzle, the mirroring of each character is obvious in retrospect, but was not obvious at first glance.
Another good example is in the hidden message puzzle "DY3DI 6974 I36G9Q4E". A computer keyboard defines the cryptographic relationship. Once you see this relationship you have your answer.
In the duck/agent puzzle, it was not even mentioned that there was a smaller circle of 1/4 the radius within the pond in which the duck could maintain an optimal position. But anyone who solved the puzzle had to deduce that this circle existed. And to do so, you merely had to realize that the duck's movement around this smaller circle would be EQUIVALENT to the movement of the agent around the pond. This equivalency was the pivot point at which I determined the duck could win the race.


5. Additional dimensions of data.

For the card trick puzzle, it was necessary to use every single opportunity to communicate information to your partner. When given 5 random cards, I immediately realized that the ordering of the cards would be one of the only ways to communicate information.
But with 4 cards there are only 24 possible arrangements. So that alone could not define a single card in a deck of 52.
One must convey additional information by doing the following...
A) use one card to define the suit.
B) use that same card to define a starting position.
C) use the arrangement of the other 3 cards to define the steps forward (1-6) from the starting position.

As you can see, the first card does double duty, conveying two pieces of information.

Another good example of layered information is the 100 Hat puzzle.
In this puzzle, the solution requires using the red/blue code to convey the even/odd status of the total hats. Then by looking at the other hats, each prisoner can determine the color of their own hat by evaluating which color would result in the correct odd/even status.


6. Depth of Concept.

For many puzzles, getting to the answer is only the starting point. A good puzzle will entice the audience to delve further into the problem to understand the concepts completely. This can be done by examining complex and difficult principles, but starting slowly, adding follow-up questions, and considering optimization of the process.
For example: After determining that the duck could escape from the agent, the next step was determining the minimum speed at which the agent could catch the duck, and to establish this, the optimal path for the duck needed to be determined. Then once all of that was discovered, a cast iron proof could be sought after. And to make this proof more clear, some illustrations would be nice.
For the Hamiltonian puzzle, once a valid path was discovered, the question became how many more paths are there? Can we prove that these are all the paths? Can we use symmetry to prove that many of the paths are identical? How many vertices must be removed to make it non-Hamiltonian?


7. Limited guesswork.

One of my least favorite puzzles is the one about the five neighbors who live in five houses with five pets, and five of this and five of that. This is because after considering all the stated facts, the only way to fill in the remaining categories is to make a guess and then determine if that will work, then if not, try again. There is no significant short-cut to this process, and so brute strenght trial and error is the only way to find your answer. The only real strategy you can employ is to keep track of all the incorrect guesses in a systematic fashion.
Some guess work makes sense for puzzling, but when all you are doing is making guesses, it does not require imagination, intelligence or that spark of inspiration.


8. Strategic Elements.

Many good puzzles ask you to consider the actions of more than one individual, each of whom will behave intelligently and respond to the actions of the others.
By adding game theory to a puzzle it becomes more complex. More logic is required to solve these sorts of puzzles. In the Duck/Agent puzzle it was necessary to consider the possibility of the agent/duck reversing directions, and to consider what would happen in those situations. The proof for the optimal path of the duck had to consider what would happen if the agent changed directions and prove definitively that such a reversal was always to the duck's advantage.

Other good examples of game theory in a puzzle are the prisoner's dillema, and the shoot out between 3 gunslingers of varying ability.

Wednesday, May 6, 2009

Some people may find this helpful.
It is a list of a the hexagons and heptagons in the 2nd Hamiltonian.

HEXAGONS:
( 1, 7, 11, 12, 19, 8)

( 2, 3, 4, 23, 24, 25)

( 4, 5, 6, 21, 22, 23)

(12, 15, 20, 26, 18, 19)


HEPTAGONS:
( 1, 2, 3, 4, 5, 6, 7)

( 1, 2, 3, 9, 13, 16, 8)

( 1, 2, 25, 24, 17, 11, 7)

( 1, 2, 25, 26, 18, 19, 8)

( 1, 7, 6, 21, 22, 16, 8)

( 2, 3, 9, 15, 20, 26, 25)

( 3, 4, 5, 10, 14, 13, 9)

( 3, 4, 23, 22, 16, 13, 9)

( 4, 5, 10, 14, 17, 24, 23)

( 5, 6, 7, 11, 17, 14, 10)

( 5, 6, 21, 20, 26, 18, 10)

( 6, 7, 11, 12, 15, 20, 21)

( 8, 16, 13, 9, 15, 12, 19)

( 8, 16, 13, 14, 10, 18, 19)

( 9, 13, 14, 17, 11, 12, 15)

( 9, 13, 16, 22, 21, 20, 15)

(10, 14, 17, 11, 12, 19, 18)

(10, 14, 17, 24, 25, 26, 18)

(13, 14, 17, 24, 23, 22, 16)

(20, 21, 22, 23, 24, 25, 26)

Tuesday, May 5, 2009

Solutions to 1st Hamiltonian

( 1, 2, 3, 4, 5, 10, 9, 8, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 15, 16, 25, 24)

( 1, 2, 3, 4, 5, 10, 9, 8, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15)

( 1, 2, 3, 4, 5, 10, 9, 8, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 24, 25, 16, 15, 21, 20, 19)

( 1, 2, 3, 4, 5, 10, 9, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 17, 14, 13, 26)

( 1, 2, 3, 4, 5, 10, 9, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 26, 13, 14, 17)

( 1, 2, 3, 4, 5, 10, 9, 8, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6)

( 1, 2, 3, 4, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22)

( 1, 2, 3, 4, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 24, 25, 26, 22, 23, 19, 20)

( 1, 2, 3, 4, 5, 10, 13, 14, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 8, 7, 6, 12, 11, 18)

( 1, 2, 3, 6, 7, 8, 4, 5, 10, 9, 16, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17, 14, 13)

( 1, 2, 3, 6, 7, 8, 4, 5, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16, 9)

( 1, 2, 3, 6, 7, 8, 9, 16, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17, 14, 13, 10, 5, 4)

( 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21)

( 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 14, 17, 18, 19, 23, 22, 26, 25, 24, 21, 20, 12, 11)

( 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 14, 17, 22, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23)

( 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23, 22, 17, 14)

( 1, 2, 3, 6, 7, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17, 14, 13, 10, 5, 4, 8, 9, 16)

( 1, 2, 11, 12, 6, 3, 4, 5, 10, 9, 16, 25, 24, 23, 22, 26, 13, 14, 17, 18, 19, 20, 21, 15, 7, 8)

( 1, 2, 11, 12, 6, 3, 4, 8, 7, 15, 21, 20, 19, 18, 17, 14, 13, 26, 22, 23, 24, 25, 16, 9, 10, 5)

( 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 5, 4, 3, 6, 7, 8, 9, 16, 15, 21, 24, 23, 22, 26, 25)

( 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 23, 24, 21, 15, 7, 6, 3)

( 1, 2, 11, 18, 17, 14, 13, 10, 5, 4, 3, 6, 7, 8, 9, 16, 15, 21, 24, 25, 26, 22, 23, 19, 20, 12)

( 1, 2, 11, 18, 17, 14, 13, 10, 5, 4, 3, 6, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16, 9, 8, 7)

( 1, 5, 4, 8, 9, 16, 15, 7, 6, 3, 2, 11, 12, 20, 21, 24, 25, 26, 22, 23, 19, 18, 17, 14, 13, 10)

( 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 18, 11, 2)

( 2, 1, 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 16, 15, 21, 24)

( 2, 1, 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16)

( 2, 1, 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15, 16, 25, 26, 22)

( 2, 1, 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 17, 22, 26, 25, 16, 15, 21, 24, 23, 19, 18, 11, 12, 20)

( 2, 1, 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 17, 22, 26, 25, 16, 15, 21, 24, 23, 19, 20, 12, 11, 18)

( 2, 1, 5, 4, 3, 6, 7, 8, 9, 16, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17, 14, 13, 10)

( 2, 1, 5, 4, 3, 6, 12, 11, 18, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26)

( 2, 1, 5, 4, 3, 6, 12, 11, 18, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19)

( 2, 1, 5, 4, 3, 6, 12, 11, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 15, 7, 8, 9, 10, 13, 14, 17)

( 2, 1, 5, 10, 9, 8, 4, 3, 6, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12)

( 2, 1, 5, 10, 9, 8, 4, 3, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15, 7)

( 2, 1, 5, 10, 9, 8, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6, 3, 4)

( 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 24, 25)

( 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 14)

( 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 11, 18, 19, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23)

( 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 18, 11)

( 2, 1, 5, 10, 9, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6, 3, 4, 8, 7, 15)

( 2, 1, 14, 13, 10, 5, 4, 3, 6, 7, 15, 21, 24, 23, 19, 20, 12, 11, 18, 17, 22, 26, 25, 16, 9, 8)

( 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15, 7, 6, 3)

( 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 6, 3, 4, 5, 10, 9, 8, 7, 15, 16, 25, 24, 23, 19, 20, 21)

( 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 6, 3, 4, 8, 7, 15, 21, 20, 19, 23, 24, 25, 16, 9, 10, 5)

( 2, 1, 14, 17, 18, 11, 12, 6, 3, 4, 5, 10, 9, 8, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13)

( 2, 1, 14, 17, 18, 11, 12, 6, 3, 4, 5, 10, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15, 7, 8, 9)

( 2, 3, 4, 8, 7, 15, 16, 9, 10, 5, 1, 14, 13, 26, 25, 24, 21, 20, 19, 23, 22, 17, 18, 11, 12, 6)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 11, 18, 17, 14, 13, 10, 9, 16, 15, 21, 20, 19, 23, 22, 26, 25, 24)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 11, 18, 17, 14, 13, 10, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 11, 18, 17, 14, 13, 10, 9, 16, 15, 21, 24, 25, 26, 22, 23, 19, 20)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 10, 13, 14)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 9, 10, 13, 14, 17, 22, 23, 24, 25, 26)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 9, 10, 13, 14, 17, 22, 26, 25, 24, 23)

( 3, 2, 1, 5, 4, 8, 7, 6, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16, 9, 10, 13, 14, 17, 18, 11)

( 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19)

( 3, 2, 1, 14, 13, 10, 5, 4, 8, 7, 6, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9)

( 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21)

( 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22, 17, 18, 11, 12, 6, 7)

( 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15, 7, 6)

( 3, 2, 1, 14, 13, 10, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22, 17, 18, 11, 12, 6, 7, 8, 4, 5)

( 3, 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 6, 7, 8, 4, 5, 10, 9, 16, 15, 21, 20, 19, 23, 24, 25)

( 3, 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 6, 7, 8, 4, 5, 10, 9, 16, 25, 24, 23, 19, 20, 21, 15)

( 3, 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 6, 7, 15, 21, 20, 19, 23, 24, 25, 16, 9, 8, 4, 5, 10)

( 3, 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 6, 7, 15, 21, 20, 19, 23, 24, 25, 16, 9, 10, 5, 4, 8)

( 3, 2, 1, 14, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 10, 5, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18)

( 3, 2, 11, 12, 6, 7, 8, 9, 10, 13, 26, 22, 23, 24, 25, 16, 15, 21, 20, 19, 18, 17, 14, 1, 5, 4)

( 3, 2, 11, 12, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19, 18, 17, 14, 1, 5, 4, 8, 9, 10, 13)

( 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 14, 1, 5, 4, 8, 9, 10, 13, 26, 22, 23, 24, 25, 16)

( 3, 2, 11, 18, 17, 14, 1, 5, 4, 8, 9, 10, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15, 7, 6, 12)

( 3, 4, 5, 10, 9, 8, 7, 6, 12, 11, 2, 1, 14, 13, 26, 22, 23, 24, 25, 16, 15, 21, 20, 19, 18, 17)

( 4, 3, 2, 1, 5, 10, 9, 8, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 15, 16, 25, 24)

( 4, 3, 2, 1, 5, 10, 9, 8, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15)

( 4, 3, 2, 1, 5, 10, 9, 8, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 24, 25, 16, 15, 21, 20, 19)

( 4, 3, 2, 1, 5, 10, 9, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 17, 14, 13, 26)

( 4, 3, 2, 1, 5, 10, 9, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 26, 13, 14, 17)

( 4, 3, 2, 1, 5, 10, 9, 8, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6)

( 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22)

( 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 24, 25, 26, 22, 23, 19, 20)

( 4, 3, 2, 1, 5, 10, 13, 14, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 8, 7, 6, 12, 11, 18)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 10, 5, 1, 14, 13, 26, 22, 17, 18, 19, 20, 21, 15, 16, 25, 24, 23)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 10, 5, 1, 14, 13, 26, 25, 24, 23, 22, 17, 18, 19, 20, 21, 15, 16)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 10, 5, 1, 14, 17, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 26, 13)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 10, 13, 26, 22, 23, 24, 25, 16, 15, 21, 20, 19, 18, 17, 14, 1, 5)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 18, 17, 14, 1, 5, 10, 13, 26, 22, 23, 24, 25)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 18, 17, 22, 23, 24, 25, 26, 13, 10, 5, 1, 14)

( 4, 3, 2, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 18, 17, 22, 23, 24, 25, 26, 13, 14, 1, 5, 10)

( 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 14, 1, 5, 10, 13, 26, 22, 23, 24, 25, 16, 9, 8)

( 4, 3, 2, 11, 18, 17, 22, 26, 13, 14, 1, 5, 10, 9, 8, 7, 6, 12, 20, 19, 23, 24, 25, 16, 15, 21)

( 4, 3, 6, 12, 11, 2, 1, 5, 10, 13, 14, 17, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 15, 7, 8, 9)

( 4, 5, 1, 14, 13, 10, 9, 8, 7, 6, 3, 2, 11, 18, 17, 22, 26, 25, 16, 15, 21, 24, 23, 19, 20, 12)

( 4, 5, 1, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26, 22, 17, 18, 19, 23, 24, 21, 20, 12, 6, 3, 2, 11)

( 4, 5, 10, 13, 14, 1, 2, 3, 6, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 8, 7)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 11, 18, 17, 14, 13, 10, 9, 16, 15, 21, 20, 19, 23, 22, 26, 25, 24)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 11, 18, 17, 14, 13, 10, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 11, 18, 17, 14, 13, 10, 9, 16, 15, 21, 24, 25, 26, 22, 23, 19, 20)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 10, 13, 14)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 9, 10, 13, 14, 17, 22, 23, 24, 25, 26)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 9, 10, 13, 14, 17, 22, 26, 25, 24, 23)

( 5, 1, 2, 3, 4, 8, 7, 6, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16, 9, 10, 13, 14, 17, 18, 11)

( 5, 1, 2, 3, 4, 8, 9, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19)

( 5, 1, 2, 11, 12, 6, 3, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 18, 19, 20, 21, 24, 23, 22, 26, 25)

( 5, 1, 2, 11, 12, 6, 3, 4, 8, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19, 18, 17, 14, 13, 10, 9)

( 5, 1, 2, 11, 12, 6, 3, 4, 8, 7, 15, 21, 20, 19, 18, 17, 14, 13, 26, 22, 23, 24, 25, 16, 9, 10)

( 5, 1, 2, 11, 12, 6, 3, 4, 8, 9, 10, 13, 14, 17, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 15, 7)

( 5, 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 9, 8, 4, 3, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21)

( 5, 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 9, 8, 4, 3, 6, 7, 15, 21, 24, 23, 22, 26, 25, 16)

( 5, 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 9, 16, 25, 26, 22, 23, 24, 21, 15, 7, 6, 3, 4, 8)

( 5, 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 9, 16, 25, 26, 22, 23, 24, 21, 15, 7, 8, 4, 3, 6)

( 5, 1, 2, 11, 18, 19, 20, 12, 6, 3, 4, 8, 7, 15, 21, 24, 23, 22, 26, 25, 16, 9, 10, 13, 14, 17)

( 5, 1, 14, 13, 10, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22, 17, 18, 11, 2, 3, 4, 8, 7, 6, 12)

( 5, 1, 14, 13, 10, 9, 16, 25, 26, 22, 17, 18, 11, 2, 3, 4, 8, 7, 6, 12, 20, 19, 23, 24, 21, 15)

( 5, 1, 14, 17, 18, 11, 2, 3, 4, 8, 7, 6, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16, 9, 10, 13)

( 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 1, 2, 11, 12, 20, 19, 23, 24, 21, 15, 16, 25, 26, 22, 17, 18)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 18, 11, 12, 20, 21, 24, 25, 26, 22, 23, 19)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 18, 19, 23, 22, 26, 25, 24, 21, 20, 12, 11)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 22, 23, 19, 18, 11, 12, 20, 21, 24, 25, 26)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 22, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23, 22, 17, 14)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17, 14, 13, 10, 9, 16)

( 6, 3, 2, 1, 5, 4, 8, 7, 15, 21, 24, 23, 19, 20, 12, 11, 18, 17, 14, 13, 10, 9, 16, 25, 26, 22)

( 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 7, 15, 21, 24, 23, 19, 20, 12, 11, 18, 17, 22, 26, 25, 16, 9)

( 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15, 7)

( 6, 3, 2, 1, 14, 13, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15, 7, 8, 4, 5, 10, 9, 16, 25)

( 6, 3, 2, 11, 12, 20, 19, 18, 17, 14, 1, 5, 4, 8, 7, 15, 21, 24, 23, 22, 26, 25, 16, 9, 10, 13)

( 6, 3, 2, 11, 12, 20, 19, 18, 17, 22, 23, 24, 21, 15, 7, 8, 4, 5, 1, 14, 13, 26, 25, 16, 9, 10)

( 6, 3, 2, 11, 12, 20, 19, 23, 22, 26, 13, 10, 9, 16, 25, 24, 21, 15, 7, 8, 4, 5, 1, 14, 17, 18)

( 6, 3, 2, 11, 12, 20, 21, 15, 7, 8, 4, 5, 1, 14, 13, 10, 9, 16, 25, 26, 22, 17, 18, 19, 23, 24)

( 6, 3, 2, 11, 12, 20, 21, 24, 23, 19, 18, 17, 22, 26, 25, 16, 9, 10, 13, 14, 1, 5, 4, 8, 7, 15)

( 6, 3, 2, 11, 18, 17, 14, 1, 5, 4, 8, 7, 15, 21, 24, 25, 16, 9, 10, 13, 26, 22, 23, 19, 20, 12)

( 6, 3, 4, 5, 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 10, 9, 16, 25, 26, 22, 23, 24, 21, 15, 7, 8)

( 6, 3, 4, 5, 10, 9, 8, 7, 15, 16, 25, 24, 21, 20, 12, 11, 2, 1, 14, 13, 26, 22, 23, 19, 18, 17)

( 6, 7, 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 18, 11, 12, 20)

( 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 16, 15, 21, 24)

( 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16)

( 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15, 16, 25, 26, 22)

( 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 22, 26, 25, 16, 15, 21, 24, 23, 19, 18, 11, 12, 20)

( 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 22, 26, 25, 16, 15, 21, 24, 23, 19, 20, 12, 11, 18)

( 7, 6, 3, 2, 1, 5, 4, 8, 9, 16, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17, 14, 13, 10)

( 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 21, 20, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19)

( 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17)

( 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22, 17, 18, 11, 12)

( 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 21, 24, 23, 19, 20, 12, 11, 18, 17, 22, 26, 25)

( 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 15, 21, 24, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23)

( 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24, 21, 15)

( 7, 6, 3, 2, 1, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21, 15, 16, 9, 8, 4, 5, 10, 13)

( 7, 6, 3, 2, 11, 12, 20, 19, 18, 17, 14, 1, 5, 4, 8, 9, 10, 13, 26, 22, 23, 24, 25, 16, 15, 21)

( 7, 6, 3, 2, 11, 12, 20, 19, 18, 17, 22, 23, 24, 21, 15, 16, 25, 26, 13, 10, 9, 8, 4, 5, 1, 14)

( 7, 6, 12, 11, 2, 3, 4, 5, 1, 14, 17, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 26, 13, 10, 9, 8)

( 7, 6, 12, 11, 18, 19, 20, 21, 15, 16, 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 22, 23, 24, 25, 26)

( 7, 6, 12, 20, 19, 18, 17, 22, 23, 24, 21, 15, 16, 25, 26, 13, 14, 1, 5, 10, 9, 8, 4, 3, 2, 11)

( 7, 8, 4, 5, 10, 13, 14, 1, 2, 3, 6, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 24, 25)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 7, 6, 12, 11, 18, 17, 14, 13, 26, 25, 24, 21, 20, 19, 23, 22)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 7, 6, 12, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 14)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 7, 6, 12, 11, 18, 19, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 7, 6, 12, 11, 18, 19, 23, 22, 17, 14, 13, 26, 25, 24, 21, 20)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 7, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 18, 11)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6, 7, 15)

( 8, 4, 3, 2, 1, 5, 10, 9, 16, 25, 24, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6, 7, 15, 21, 20, 19)

( 8, 4, 3, 2, 11, 12, 6, 7, 15, 16, 9, 10, 5, 1, 14, 13, 26, 25, 24, 21, 20, 19, 23, 22, 17, 18)

( 8, 4, 3, 2, 11, 12, 6, 7, 15, 16, 9, 10, 5, 1, 14, 13, 26, 25, 24, 23, 22, 17, 18, 19, 20, 21)

( 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 14, 1, 5, 10, 9, 16, 25, 24, 23, 22, 26, 13)

( 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 14, 1, 5, 10, 13, 26, 22, 23, 24, 25, 16, 9)

( 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 22, 23, 24, 25, 16, 9, 10, 5, 1, 14, 13, 26)

( 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 22, 23, 24, 25, 26, 13, 14, 1, 5, 10, 9, 16)

( 8, 4, 3, 2, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 14, 1, 5, 10, 9, 16, 15, 7, 6, 12)

( 8, 4, 5, 1, 14, 13, 10, 9, 16, 15, 7, 6, 3, 2, 11, 12, 20, 21, 24, 25, 26, 22, 23, 19, 18, 17)

( 8, 7, 6, 3, 4, 5, 1, 2, 11, 12, 20, 21, 15, 16, 9, 10, 13, 14, 17, 18, 19, 23, 22, 26, 25, 24)

( 8, 7, 6, 12, 11, 2, 3, 4, 5, 1, 14, 13, 26, 25, 24, 23, 22, 17, 18, 19, 20, 21, 15, 16, 9, 10)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 16, 25, 26, 22, 23, 19, 20, 21, 24)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 15, 7, 6, 12, 11)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 22, 26, 25, 16, 15, 7, 6, 12, 11, 18, 19, 20, 21, 24, 23)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 22, 26, 25, 16, 15, 7, 6, 12, 11, 18, 19, 23, 24, 21, 20)

( 9, 8, 4, 3, 2, 1, 5, 10, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15, 7, 6, 12, 11, 18, 17, 14)

( 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 10, 5, 1, 14, 17, 18)

( 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 16, 25, 24, 23, 22, 26, 13, 10, 5, 1, 14, 17, 18, 19, 20, 21)

( 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 16, 25, 26, 13, 10, 5, 1, 14, 17, 18, 19, 20, 21, 24, 23, 22)

( 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19, 18, 17, 14, 1, 5, 10, 13)

( 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 14, 1, 5, 10, 13, 26, 22, 23, 24, 25, 16)

( 9, 8, 4, 3, 2, 11, 18, 17, 14, 1, 5, 10, 13, 26, 22, 23, 19, 20, 21, 24, 25, 16, 15, 7, 6, 12)

( 9, 8, 4, 5, 10, 13, 26, 22, 23, 19, 18, 11, 12, 20, 21, 24, 25, 16, 15, 7, 6, 3, 2, 1, 14, 17)

( 9, 8, 7, 6, 3, 4, 5, 10, 13, 14, 1, 2, 11, 12, 20, 21, 24, 23, 19, 18, 17, 22, 26, 25, 16, 15)

( 9, 8, 7, 6, 12, 11, 2, 3, 4, 5, 1, 14, 17, 18, 19, 20, 21, 15, 16, 25, 24, 23, 22, 26, 13, 10)

( 9, 10, 5, 1, 14, 13, 26, 22, 17, 18, 11, 2, 3, 4, 8, 7, 6, 12, 20, 19, 23, 24, 21, 15, 16, 25)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 17, 14, 13, 26, 22, 23, 19, 20, 21, 24, 25)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 17, 14, 13, 26, 25, 24, 21, 20, 19, 23, 22)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 14)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 19, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 19, 23, 22, 17, 14, 13, 26, 25, 24, 21, 20)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 18, 11)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6, 7, 15)

(10, 5, 1, 2, 3, 4, 8, 9, 16, 25, 24, 23, 22, 26, 13, 14, 17, 18, 11, 12, 6, 7, 15, 21, 20, 19)

(10, 5, 1, 2, 11, 12, 20, 19, 18, 17, 14, 13, 26, 22, 23, 24, 25, 16, 9, 8, 4, 3, 6, 7, 15, 21)

(10, 5, 1, 14, 13, 26, 22, 17, 18, 11, 2, 3, 4, 8, 9, 16, 25, 24, 23, 19, 20, 21, 15, 7, 6, 12)

(10, 5, 1, 14, 13, 26, 22, 23, 19, 20, 12, 6, 7, 15, 21, 24, 25, 16, 9, 8, 4, 3, 2, 11, 18, 17)

(10, 5, 1, 14, 13, 26, 25, 16, 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 22, 23, 24)

(10, 5, 1, 14, 13, 26, 25, 24, 21, 15, 7, 6, 12, 20, 19, 23, 22, 17, 18, 11, 2, 3, 4, 8, 9, 16)

(10, 5, 1, 14, 17, 18, 11, 2, 3, 4, 8, 9, 16, 25, 24, 21, 15, 7, 6, 12, 20, 19, 23, 22, 26, 13)

(10, 5, 4, 3, 6, 7, 8, 9, 16, 15, 21, 24, 25, 26, 13, 14, 1, 2, 11, 12, 20, 19, 23, 22, 17, 18)

(10, 9, 8, 4, 5, 1, 2, 3, 6, 7, 15, 16, 25, 24, 21, 20, 12, 11, 18, 19, 23, 22, 17, 14, 13, 26)

(11, 2, 1, 5, 4, 3, 6, 12, 20, 19, 18, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26, 22, 23, 24, 21)

(11, 2, 1, 5, 4, 3, 6, 12, 20, 19, 18, 17, 14, 13, 10, 9, 8, 7, 15, 21, 24, 23, 22, 26, 25, 16)

(11, 2, 1, 5, 4, 3, 6, 12, 20, 21, 24, 23, 19, 18, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26, 22)

(11, 2, 1, 5, 4, 3, 6, 12, 20, 21, 24, 23, 19, 18, 17, 22, 26, 25, 16, 15, 7, 8, 9, 10, 13, 14)

(11, 2, 1, 5, 4, 3, 6, 12, 20, 21, 24, 23, 22, 26, 25, 16, 15, 7, 8, 9, 10, 13, 14, 17, 18, 19)

(11, 2, 1, 5, 4, 3, 6, 12, 20, 21, 24, 25, 16, 15, 7, 8, 9, 10, 13, 14, 17, 18, 19, 23, 22, 26)

(11, 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 18)

(11, 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 25, 26, 22, 23, 19, 18, 17, 14, 13)

(11, 2, 1, 5, 10, 9, 16, 25, 24, 21, 15, 7, 8, 4, 3, 6, 12, 20, 19, 18, 17, 14, 13, 26, 22, 23)

(11, 2, 1, 5, 10, 9, 16, 25, 24, 23, 22, 26, 13, 14, 17, 18, 19, 20, 21, 15, 7, 8, 4, 3, 6, 12)

(11, 2, 1, 14, 13, 10, 5, 4, 3, 6, 12, 20, 21, 15, 7, 8, 9, 16, 25, 26, 22, 17, 18, 19, 23, 24)

(11, 2, 1, 14, 13, 10, 5, 4, 3, 6, 12, 20, 21, 24, 23, 19, 18, 17, 22, 26, 25, 16, 9, 8, 7, 15)

(11, 2, 1, 14, 13, 26, 22, 17, 18, 19, 23, 24, 21, 20, 12, 6, 3, 4, 5, 10, 9, 8, 7, 15, 16, 25)

(11, 12, 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 18, 19, 23, 22, 26, 25, 24, 21, 20)

(11, 12, 6, 3, 2, 1, 14, 13, 26, 22, 23, 24, 25, 16, 9, 10, 5, 4, 8, 7, 15, 21, 20, 19, 18, 17)

(12, 6, 3, 2, 11, 18, 17, 14, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 26, 22, 23, 19, 20, 21, 24, 25)

(12, 6, 3, 2, 11, 18, 17, 14, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 26, 25, 24, 21, 20, 19, 23, 22)

(12, 6, 3, 2, 11, 18, 17, 14, 1, 5, 4, 8, 7, 15, 21, 20, 19, 23, 22, 26, 13, 10, 9, 16, 25, 24)

(12, 6, 3, 2, 11, 18, 17, 14, 1, 5, 4, 8, 7, 15, 21, 24, 25, 16, 9, 10, 13, 26, 22, 23, 19, 20)

(12, 6, 3, 2, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 10, 9, 16, 15, 7, 8, 4, 5, 1, 14)

(12, 6, 3, 2, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 7, 8, 4, 5, 1, 14, 13, 10, 9, 16)

(12, 6, 3, 2, 11, 18, 19, 20, 21, 15, 7, 8, 4, 5, 1, 14, 17, 22, 23, 24, 25, 16, 9, 10, 13, 26)

(12, 6, 3, 2, 11, 18, 19, 20, 21, 15, 7, 8, 4, 5, 1, 14, 17, 22, 26, 13, 10, 9, 16, 25, 24, 23)

(12, 6, 3, 4, 5, 1, 2, 11, 18, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 19)

(12, 6, 3, 4, 5, 1, 2, 11, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 15, 7, 8, 9, 10, 13, 14, 17)

(12, 6, 7, 8, 4, 3, 2, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26, 13, 14, 1, 5, 10, 9, 16, 15)

(12, 6, 7, 8, 4, 3, 2, 11, 18, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 10, 5, 1, 14, 13)

(12, 11, 2, 1, 5, 10, 9, 8, 4, 3, 6, 7, 15, 16, 25, 24, 21, 20, 19, 23, 22, 26, 13, 14, 17, 18)

(12, 11, 2, 1, 5, 10, 9, 8, 4, 3, 6, 7, 15, 16, 25, 24, 23, 22, 26, 13, 14, 17, 18, 19, 20, 21)

(13, 10, 5, 1, 14, 17, 18, 11, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 20, 19, 23, 22, 26, 25, 24, 21)

(13, 10, 5, 1, 14, 17, 18, 11, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 20, 21, 24, 25, 26, 22, 23, 19)

(13, 10, 5, 1, 14, 17, 18, 11, 2, 3, 4, 8, 9, 16, 25, 24, 21, 15, 7, 6, 12, 20, 19, 23, 22, 26)

(13, 10, 5, 1, 14, 17, 18, 11, 2, 3, 4, 8, 9, 16, 25, 26, 22, 23, 19, 20, 12, 6, 7, 15, 21, 24)

(13, 10, 5, 1, 14, 17, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 9, 8, 4, 3, 2, 11, 12, 6, 7, 15)

(13, 10, 5, 1, 14, 17, 22, 26, 25, 16, 9, 8, 4, 3, 2, 11, 18, 19, 20, 12, 6, 7, 15, 21, 24, 23)

(13, 10, 5, 1, 14, 17, 22, 26, 25, 16, 9, 8, 4, 3, 2, 11, 18, 19, 23, 24, 21, 15, 7, 6, 12, 20)

(13, 10, 5, 4, 3, 2, 1, 14, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 22)

(13, 10, 5, 4, 3, 2, 1, 14, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 8, 7, 6, 12, 11, 18)

(13, 10, 5, 4, 3, 6, 12, 20, 19, 23, 24, 21, 15, 7, 8, 9, 16, 25, 26, 22, 17, 18, 11, 2, 1, 14)

(13, 10, 9, 8, 4, 5, 1, 14, 17, 18, 19, 20, 12, 11, 2, 3, 6, 7, 15, 21, 24, 23, 22, 26, 25, 16)

(13, 14, 1, 2, 3, 6, 7, 8, 4, 5, 10, 9, 16, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17)

(13, 14, 1, 2, 3, 6, 7, 8, 4, 5, 10, 9, 16, 15, 21, 24, 23, 19, 20, 12, 11, 18, 17, 22, 26, 25)

(14, 1, 2, 3, 4, 5, 10, 13, 26, 22, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19, 23, 24, 25)

(14, 1, 2, 3, 4, 5, 10, 13, 26, 22, 17, 18, 11, 12, 6, 7, 8, 9, 16, 25, 24, 23, 19, 20, 21, 15)

(14, 1, 2, 3, 4, 5, 10, 13, 26, 25, 24, 21, 15, 16, 9, 8, 7, 6, 12, 11, 18, 17, 22, 23, 19, 20)

(14, 1, 2, 3, 4, 5, 10, 13, 26, 25, 24, 23, 19, 20, 21, 15, 16, 9, 8, 7, 6, 12, 11, 18, 17, 22)

(14, 1, 2, 3, 4, 5, 10, 13, 26, 25, 24, 23, 22, 17, 18, 11, 12, 6, 7, 8, 9, 16, 15, 21, 20, 19)

(14, 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23, 22, 17)

(14, 1, 2, 3, 6, 7, 15, 21, 24, 25, 16, 9, 8, 4, 5, 10, 13, 26, 22, 17, 18, 11, 12, 20, 19, 23)

(14, 1, 2, 11, 12, 6, 3, 4, 5, 10, 13, 26, 25, 16, 9, 8, 7, 15, 21, 20, 19, 18, 17, 22, 23, 24)

(14, 1, 2, 11, 12, 6, 3, 4, 5, 10, 13, 26, 25, 24, 23, 22, 17, 18, 19, 20, 21, 15, 7, 8, 9, 16)

(14, 1, 2, 11, 12, 20, 19, 18, 17, 22, 23, 24, 25, 26, 13, 10, 5, 4, 3, 6, 7, 8, 9, 16, 15, 21)

(14, 13, 10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 17, 22, 23, 19, 20, 21, 24, 25, 26)

(14, 13, 10, 5, 1, 2, 11, 12, 20, 19, 23, 24, 21, 15, 7, 6, 3, 4, 8, 9, 16, 25, 26, 22, 17, 18)

(15, 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24, 21)

(15, 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 21, 24, 23, 19)

(15, 7, 6, 3, 2, 1, 14, 17, 22, 23, 19, 18, 11, 12, 20, 21, 24, 25, 16, 9, 8, 4, 5, 10, 13, 26)

(15, 7, 6, 3, 2, 1, 14, 17, 22, 23, 19, 18, 11, 12, 20, 21, 24, 25, 26, 13, 10, 5, 4, 8, 9, 16)

(15, 7, 6, 3, 2, 1, 14, 17, 22, 26, 13, 10, 5, 4, 8, 9, 16, 25, 24, 21, 20, 12, 11, 18, 19, 23)

(15, 7, 6, 3, 4, 8, 9, 16, 25, 26, 22, 17, 14, 13, 10, 5, 1, 2, 11, 12, 20, 21, 24, 23, 19, 18)

(15, 7, 6, 3, 4, 8, 9, 16, 25, 26, 22, 23, 19, 18, 17, 14, 13, 10, 5, 1, 2, 11, 12, 20, 21, 24)

(15, 7, 6, 12, 11, 2, 3, 4, 8, 9, 16, 25, 26, 13, 10, 5, 1, 14, 17, 18, 19, 20, 21, 24, 23, 22)

(15, 7, 6, 12, 11, 18, 19, 20, 21, 24, 23, 22, 26, 25, 16, 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17)

(15, 16, 9, 8, 7, 6, 3, 4, 5, 10, 13, 14, 1, 2, 11, 12, 20, 21, 24, 23, 19, 18, 17, 22, 26, 25)

(15, 16, 9, 8, 7, 6, 12, 11, 18, 19, 23, 22, 17, 14, 1, 2, 3, 4, 5, 10, 13, 26, 25, 24, 21, 20)

(16, 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 21, 20, 19, 23, 22, 26, 25, 24)

(16, 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 21, 20, 19, 23, 24, 25, 26, 22)

(16, 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 18, 11, 12, 6, 7, 15, 21, 24, 25, 26, 22, 23, 19, 20)

(16, 9, 8, 4, 3, 2, 1, 5, 10, 13, 14, 17, 22, 26, 25, 24, 23, 19, 20, 21, 15, 7, 6, 12, 11, 18)

(16, 9, 8, 4, 3, 2, 11, 12, 6, 7, 15, 21, 20, 19, 18, 17, 14, 1, 5, 10, 13, 26, 22, 23, 24, 25)

(16, 9, 8, 4, 3, 2, 11, 18, 19, 20, 12, 6, 7, 15, 21, 24, 25, 26, 13, 10, 5, 1, 14, 17, 22, 23)

(16, 9, 8, 4, 5, 10, 13, 14, 1, 2, 3, 6, 7, 15, 21, 20, 12, 11, 18, 17, 22, 26, 25, 24, 23, 19)

(16, 9, 8, 4, 5, 10, 13, 14, 1, 2, 3, 6, 7, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 26, 22, 17)

(16, 15, 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 25, 24, 21)

(16, 15, 7, 6, 3, 2, 1, 5, 4, 8, 9, 10, 13, 14, 17, 22, 23, 19, 18, 11, 12, 20, 21, 24, 25, 26)

(17, 14, 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 26, 22, 23, 19, 18, 11, 12, 20, 21, 24, 25)

(17, 14, 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23, 22)

(17, 14, 1, 2, 3, 6, 7, 15, 21, 20, 12, 11, 18, 19, 23, 22, 26, 13, 10, 5, 4, 8, 9, 16, 25, 24)

(17, 14, 1, 2, 3, 6, 7, 15, 21, 24, 25, 16, 9, 8, 4, 5, 10, 13, 26, 22, 23, 19, 18, 11, 12, 20)

(17, 14, 1, 2, 3, 6, 7, 15, 21, 24, 25, 16, 9, 8, 4, 5, 10, 13, 26, 22, 23, 19, 20, 12, 11, 18)

(17, 14, 1, 2, 11, 18, 19, 20, 12, 6, 3, 4, 5, 10, 13, 26, 22, 23, 24, 25, 16, 9, 8, 7, 15, 21)

(17, 14, 13, 10, 5, 1, 2, 3, 4, 8, 9, 16, 15, 7, 6, 12, 11, 18, 19, 20, 21, 24, 25, 26, 22, 23)

(17, 14, 13, 10, 9, 8, 4, 5, 1, 2, 3, 6, 7, 15, 16, 25, 24, 21, 20, 12, 11, 18, 19, 23, 22, 26)

(17, 14, 13, 10, 9, 8, 4, 5, 1, 2, 3, 6, 7, 15, 16, 25, 26, 22, 23, 24, 21, 20, 12, 11, 18, 19)

(18, 11, 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 19, 23, 22, 17, 14, 13, 26, 25, 24, 21)

(18, 11, 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19)

(18, 11, 2, 1, 5, 10, 9, 16, 25, 24, 21, 15, 7, 8, 4, 3, 6, 12, 20, 19, 23, 22, 17, 14, 13, 26)

(18, 11, 2, 1, 5, 10, 9, 16, 25, 26, 13, 14, 17, 22, 23, 19, 20, 12, 6, 3, 4, 8, 7, 15, 21, 24)

(18, 11, 2, 1, 14, 17, 22, 26, 13, 10, 5, 4, 3, 6, 12, 20, 19, 23, 24, 21, 15, 7, 8, 9, 16, 25)

(18, 11, 12, 6, 3, 2, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 14, 17, 22, 26, 25, 24, 21, 20, 19, 23)

(18, 11, 12, 6, 7, 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 21, 20, 19, 23, 24, 25, 26, 13, 14, 17, 22)

(18, 11, 12, 6, 7, 8, 4, 3, 2, 1, 5, 10, 9, 16, 15, 21, 24, 25, 26, 13, 14, 17, 22, 23, 19, 20)

(19, 18, 11, 2, 1, 5, 4, 3, 6, 12, 20, 21, 24, 23, 22, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26)

(19, 18, 11, 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 23, 22, 17, 14, 13, 26, 25)

(19, 18, 11, 2, 1, 5, 10, 9, 16, 15, 7, 8, 4, 3, 6, 12, 20, 21, 24, 25, 26, 13, 14, 17, 22, 23)

(19, 18, 11, 2, 1, 5, 10, 9, 16, 25, 26, 13, 14, 17, 22, 23, 24, 21, 15, 7, 8, 4, 3, 6, 12, 20)

(19, 18, 17, 14, 1, 2, 11, 12, 20, 21, 15, 16, 9, 8, 7, 6, 3, 4, 5, 10, 13, 26, 25, 24, 23, 22)

(19, 18, 17, 14, 1, 5, 4, 8, 9, 10, 13, 26, 22, 23, 24, 25, 16, 15, 7, 6, 3, 2, 11, 12, 20, 21)

(19, 18, 17, 14, 13, 10, 5, 1, 2, 11, 12, 20, 21, 15, 7, 6, 3, 4, 8, 9, 16, 25, 26, 22, 23, 24)

(20, 12, 6, 3, 2, 11, 18, 19, 23, 22, 17, 14, 1, 5, 4, 8, 7, 15, 16, 9, 10, 13, 26, 25, 24, 21)

(20, 12, 6, 3, 2, 11, 18, 19, 23, 22, 17, 14, 1, 5, 4, 8, 7, 15, 21, 24, 25, 16, 9, 10, 13, 26)

(20, 12, 6, 3, 2, 11, 18, 19, 23, 24, 21, 15, 7, 8, 4, 5, 1, 14, 17, 22, 26, 13, 10, 9, 16, 25)

(20, 12, 6, 3, 4, 5, 10, 13, 26, 25, 16, 9, 8, 7, 15, 21, 24, 23, 19, 18, 11, 2, 1, 14, 17, 22)

(20, 12, 11, 2, 1, 5, 4, 3, 6, 7, 8, 9, 10, 13, 14, 17, 18, 19, 23, 22, 26, 25, 16, 15, 21, 24)

(20, 12, 11, 2, 1, 14, 13, 10, 5, 4, 3, 6, 7, 8, 9, 16, 15, 21, 24, 25, 26, 22, 17, 18, 19, 23)

(21, 15, 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 24, 23, 19, 20, 12, 11, 18, 17, 22, 26)

(21, 15, 7, 6, 3, 2, 1, 14, 13, 10, 5, 4, 8, 9, 16, 25, 26, 22, 17, 18, 11, 12, 20, 19, 23, 24)

(21, 15, 7, 6, 3, 2, 1, 14, 17, 18, 11, 12, 20, 19, 23, 24, 25, 16, 9, 8, 4, 5, 10, 13, 26, 22)

(21, 15, 16, 9, 8, 7, 6, 3, 4, 5, 10, 13, 14, 1, 2, 11, 12, 20, 19, 18, 17, 22, 26, 25, 24, 23)

(21, 15, 16, 9, 10, 5, 1, 14, 13, 26, 22, 17, 18, 11, 2, 3, 4, 8, 7, 6, 12, 20, 19, 23, 24, 25)

(22, 17, 14, 1, 2, 3, 6, 7, 15, 16, 9, 8, 4, 5, 10, 13, 26, 25, 24, 21, 20, 12, 11, 18, 19, 23)

(22, 17, 14, 1, 2, 3, 6, 7, 15, 21, 20, 12, 11, 18, 19, 23, 24, 25, 16, 9, 8, 4, 5, 10, 13, 26)

(22, 17, 18, 11, 2, 3, 4, 8, 7, 6, 12, 20, 19, 23, 24, 21, 15, 16, 9, 10, 5, 1, 14, 13, 26, 25)

(22, 17, 18, 11, 12, 6, 3, 2, 1, 14, 13, 26, 25, 16, 9, 10, 5, 4, 8, 7, 15, 21, 20, 19, 23, 24)

(23, 19, 18, 11, 2, 1, 5, 4, 3, 6, 12, 20, 21, 24, 25, 16, 15, 7, 8, 9, 10, 13, 14, 17, 22, 26)

(23, 19, 18, 11, 2, 1, 14, 17, 22, 26, 13, 10, 5, 4, 3, 6, 12, 20, 21, 15, 7, 8, 9, 16, 25, 24)

(23, 19, 20, 12, 6, 7, 8, 4, 3, 2, 11, 18, 17, 22, 26, 13, 14, 1, 5, 10, 9, 16, 15, 21, 24, 25)

(24, 21, 15, 7, 6, 3, 2, 1, 14, 17, 18, 11, 12, 20, 19, 23, 22, 26, 13, 10, 5, 4, 8, 9, 16, 25)

(24, 21, 20, 12, 6, 3, 4, 5, 1, 2, 11, 18, 19, 23, 22, 17, 14, 13, 10, 9, 8, 7, 15, 16, 25, 26)

(25, 16, 9, 8, 4, 3, 2, 11, 18, 19, 20, 12, 6, 7, 15, 21, 24, 23, 22, 17, 14, 1, 5, 10, 13, 26)