(http://cf.ltkcdn.net/online/images/std/154036-400x266-Jigsaw_puzzle_istock.jpg)
War is really just one big puzzle. So why not train for it with some smaller puzzles?
Welcome to the Guilds Puzzle League! The rules of the league are simple. Each round, we'll post a new puzzle (or multiple puzzles, but then the difficulty will be tweaked accordingly). Each guild which manages to properly solve the puzzle(s) for the round advance and get to play in the next round! Of course, this might devolve into an eventual lock, so we have a bonus feature: Sudden Death Rounds! A Sudden Death Round will involve more complex puzzles, which will be qualitatively graded. The team which does the worst will be eliminated (so there will be a guaranteed elimination). Some specifics:
1. Guilds will have to sign up to play. Please sign up in this thread by posting, 'My guild, [Insert Guild Name Here], will participate in the Guilds Puzzle League!'. You should try to have at least 2-3 active people willing to participate in the league, in order to prevent inactivity from striking you down.
2. Rounds, both standard and Sudden Death, will last 1 week. However, Sudden Death rounds will have 5 days for submissions and 48 hours for judging.
3. The difficulty of puzzles will increase as the League progresses, and the prizes will depend on the number of weeks the league lasts.
Feel free to ask any questions in this thread, thank you!
Surviving Guilds are:
Bunchie Peace Embassy
Rainbros
OtyUnity
The Graveyard
Thunderbolts
AbomiNation
Round 6
"The Final Trail, where could that be?"
"No clue."
"Of course we have clues! That's what we've been after this whole goose chase!"
"Then let's lay out the clues."
"But what if the others find out?"
"Then they will have to be prepared to be puzzled." (The sound of a drum roll could be heard echoing in the distance)
THE TASK
Send a puzzle to the Guildmasters (http://elementscommunity.org/forum/pm/?sa=send;u=7892,7603) within 5 days, with its solution in spoiler tags. The puzzle can be of any form but it must be solvable with all the information provided. You should also try to avoid using the puzzle forms from previous rounds, and try to make a creative and challenging Puzzle.
After all the puzzles have been submitted, they will be made public and the two other teams will have to try to solve them within TWO days (If you feel like two days is insufficient, please post saying so in this thread). You earn 1 point for each team that cannot solve your puzzle, and 1 point for each puzzle that you solve successfully. The team with the lowest score will be eliminated.
This will be a sudden elimination round, so in case of a tie we'll consider the quality of the Puzzle you chose. Puzzles will be graded on two aspects: How creative they are (a.k.a. is it simply a copy of a common pen-and-paper puzzle? Or did the team come up with something never seen before?) and how challenging they are (how difficult they are to solve). Good to you all, and happy puzzling!
Time left for Round 6: None
Round 5
The interior of the pyramid had an eerie glow to it, as the torchlight glared off the ancient walls made of elements unknown. The Guildmates navigated through the hidden doors and thankfully avoided all the booby traps and mummies. After an hour of traversing the boring pyramid, they finally reached the fun part: the primary burial chamber.
A huge sarcophagus was placed at the center of the chamber, though it was still too small to accommodate any valuable treasure. So they searched the rest of the room, until they found an engraved little cornerstone. Ancient Elementals didn't have hieroglyphics, but they did have their own weird code. The last will and testament of the entombed lord was not for all to see.
THE TASKThe code follows this key:
a=1, b=10, c=11, d=100, e=101, f=110, g=111, h=1000, i=1001, j=1010, k=1011, l=1100, m=1101, n=1110, o=1111, p=10000, q=10001, r=10010, s=10011, t=10100, u=10101, v=10110, w=10111, x=11000, y=11001, z=11010.
The code is as follows:
101001000100110011 100110011 101001000101 110011001110100 10111111110010100 1111110 1100111110010100 110101111011010110010100111101111.
1001110 11001111110101 101111001100111000 101001111 11010011110100, 100111011011011 11111010110100 101001000101 1101001111011100 1010010010110011100.
101001111 10010011001111111110010100 11110100 1011010010110010111010011010011001, 11110100 101011100111111110100!
111001100 110011111001010010011 1101101011001110100 1000101101100 101001000101 11111001100, 11110100 111010110111 11110010101110100 10111111110010101110011 1101101011001110100 10101 10011111110101.
11110100 11101111 10100100101011100111010110010101 110111110010 11001111110101. 101001000101 1111011101 100110011 1 11001001101.
Also, if you can find any insights on how to solve this puzzle elegantly, include it in your PM! The team with the most elegant insight will earn Immunity next round if it is a Sudden Death.
Find the solution (plus any insights) and send it to the Guildmasters (http://elementscommunity.org/forum/pm/?sa=send;u=7892,7603) within a week.
Time left for Round 5: NoneThe solution:
This is the last word of lord Zanzarino.
If you wish to find, seek out the final trail.
To discord and eternity, and beyond!
All lords must heed the call, and new great works must be done.
And no treasure for you. The cake is a lie.
The gem is a lie is also acceptable for the last sentence, though it obviously makes no sense.
Round 4
The Guildmates braved the horrors of the maze for a long fortnight without any food, water or light, walking on and on through the shifting walls... ok 10 days isn't in the territory of a fortnight, not even a short one. But half of them perished in the journey, so it was a pretty significant period of time, ok?
Finally they reached a pyramid, one which thankfully seemed to have stable walls. They sighed, wistful that they were the ones who had made it this far under such unfortunate circumstances. With one final glance at each other, they took the first step forward together.
That's when some of the Ghosts of the Past crept up.
We're sorry to spoil the mood and all, but this is an outrageous hazard of a trip and you'll have to do some more stuff with your heads before going forward.
"But we just got through so much hardship..."
Nothing very mentally challenging though, am I right? I kept telling that guy he should've put a kept more of the Ctulhu mythos around. All that brainwashing and insanity really stimulates craniums.
"This isn't particularly fair, is it?"
Hey the narrator is now pulling an RR, you think that's fair? Think of how much better our dialogue could've been.
"But he's not very good at pulling off an RR."
That's the worst part.
The entrance to the pyramid seemed to have another maze engraved on it, but on closer inspection it turned out to be a sudoku. Easy enough for hardened puzzle-solvers, but looks can be deceiving at times.
THE TASKThe Sudoku is as follows:
(http://i.imgur.com/afLe2WK.png)
Find the solution and send it to the Guildmasters (http://elementscommunity.org/forum/pm/?sa=send;u=7892,7603) within a week. We hope to avoid further delays like this one in the future!
Time left for Round 4: NoneThe solution:
(http://up.picr.de/23672284ht.jpg)
Round 3
"Ready?" The guildmates glanced at each other, none daring to imagine what horrors would be committed if the button was pressed. They had assembled all the keys to activate the procedure, but communication with Hackers was still strictly forbidden.
"Well it's only to save the Lord" They whispered to themselves, and someone walked up and pressed the button.
The hackers arched their back and looked upwards, as if they were staring into the face of God. But their eyes had been replaced by blank, sunken hollows, and through these hollows they turned towards the Guildmates.
"You seek the Looord, little elementalists? Do you seek our unending power? Or have you come to gloat, have you come to see what hell looks like?"
"Please, we have just come to find the Elemental Lord." The one who had pressed the button whimpered.
"
Heh, you should've chosen one of the other options. You lot don't look fit enough to traverse the forgotten Minotaur's Maze." With that, the bodies fell limp again.
You know that the Minotaur was the originator of all the Ghosts of the Past which haunted the deserts of Thyme, but its Maze was a long-lost legend. "Well now we know it exists. And we shall find it!"
~*~
After several days of searching you stumble upon the Maze. Almost too easily, in fact. As you try to enter through the gateway though, you find that only one of you can enter at a time. Still nothing too hard, you'll just have to cross one at a time.
As you enter, you find yourself in a large room. Large, but not gargantuan to fit the legendary description of the maze. As you walk through the twists and turns, you find that there is a Gateway at the exact midpoint of each wall, similar to the one you just entered through. You walk up to on gateway, and push through. As you barge in to the next room, you discover to your horror that the walls are turning...
THE TASKThe original configuration of the Maze is as follows:
(http://i.imgur.com/hqf6YWN.png)
The red walls are immovable, and the black walls are the moveable walls. The brown lines between rooms are Gateways. Whenever you pass through a Gateway, ALL the black walls in each room move 90 degrees in either clockwise or anticlockwise direction. This direction is constant for each room. So now you must pass through this grid from the Top left corner to the bottom right corner. Also, you must transmit a message back to your comrades telling them how to traverse the Maze. Knowing that the maze might very well change its initial configuration, it would be best if you included detailed steps on how to solve the maze from any initial configuration.
This maze could also be used to stop those thieving scum back town from breaking into your Guild! Send a message back to your guildmates on how to create such a grid. You also have to construct one yourself, making it as complex (or have as few solutions) as possible, but it must fit on a 9x9 grid like the one shown above.
Since this is a
Sudden Death round , entries will be judged by the Guildmasters. Ties will be broken by:
1. Who takes the smallest no. of steps to solve the given maze (Going from one 1x1 square in the 9x9 grid to another counts a step e.g. in the first room, going from the top left to bottom right spot takes 4 steps)
2. The complexity of the constructed Maze. Be sure to keep it within a 9x9 grid!
3. The descriptions present on solving and constructing such Mazes.
Find the solution, make your own grid and describe the methods in detail! Send it all to the Guildmasters (http://elementscommunity.org/forum/pm/?sa=send;u=7892,7603) within FIVE DAYS. As it is sudden death, we will need some time, so do try to send them in as fast as you can!
Time left for Round 3: NoneA simple solution to the maze was:
The Middle-Top room rotates clockwise. The rest turn counterclockwise.
ees(e)se(s)essw(s)es(e)see
which is 18 steps.
Round 2
The news of the elemental Lord's departure spread like wildfire. People from all over the land lamented his departure, and many started planning expeditions to bring him back (the fact that he had gone away to retire was beside the point). As the people dreamt of old times, dark forces started gathering and hatched a plot to demolish the Elemental lands while their leader was away. They set citizen against citizen, brother against brother, even Guild against guild! The dark forces planned to snatch power amidst the confusion. But several of the most loyal guilds caught wind of their plans. Helpless against the confusion of their own countrymen, they set out in order to retrieve the Lord and return the Elemental lands to its former glory.
They trekked for 7 days and 6 nights through the deserts of Thyme. At the time of sunset on the 7th day, their paths converged at what appeared to be a huge palace constructed of the finest glass. Entering the palace, they found pristine white walls covering a research center, lined with various test tubes and research notes. And at the center, hidden from plain view were four limp bodies. Upon closer investigation they turned out to be Elementals, but each having their own grotesque feature. The Guildmates realized in horror that they were looking at four hackers...
THE TASKA sudden flash of clarity sweeps through all of you, and you find that the Lord had been here a few days before and had experimented and punished these hackers standing exactly where you stand right now. You know that these 4 each have a name, each used a deck with two key cards, each developed a hack and used that hack versus a specific False God. In your flash of clarity, you also realize certain facts about how the hackers are positioned:
1. The person that used Gravity pillars as his stalling strategy is next to the person who hacked to procure Gravity marks.
2. The person that has Mutation in his deck is not next to the person who has Skeleton.
3. The person who used a hack to boost his Electrum is next to the one who attacked Hermes.
4. The person that attacked Osiris is not next to the one that uses Reverse Time.
5. Bran is next to the person using Flooding.
Investigating around the lab, you find some research notes on the hackers:
6. The person who attacked Ferox hacked to procure Holy Cow cards, and used them against her.
7. Sean hacked in order to have a stylish Top Hat near his HP bar.
8. Will is fond of using Mindgates in his deck.
9. Mark used his hacks to target Hecate.
10. The person using Shard of Void is the first from the left.
Finally, you uncover the bed used by the Lord during his stay in the palace. For his five day stay he had noted five pieces of information about the hackers, one for each day:
11. The person 3rd from the right uses Skeleton.
12. The person 2nd from the right uses Gravity Pillars.
13. The person who targetted Osiris is 4th from the left.
14. The person who used Mutation also used Flooding in his deck.
15. Sean did not attack Hermes.
Using this information, you must deduce the name, targetted False God, hack and two cards in deck for each person. If you can find these, then maybe you can awaken them and learn more about where the lord has disappeared to. Find out the information and send it to the Guildmasters (http://elementscommunity.org/forum/pm/?sa=send;u=7892,7603) within one week.
Time left for Round 2: NoneName | Mark | Will | Bran | Sean |
FG | Hecate | Hermes | Ferox | Osiris |
Card 1 | SoV | Skeleton | Gravity pillar | Mutation |
Card 2 | Reverse Time | Mindgate | Holy Cow | Flooding |
Hack | Electrum | Gravity mark | Holy Cow | Top hat |
Round 1
The Lord of the elementals was a beloved one. His long reign of 40 years had seen only happiness and prosperity. Guilds had been established peacefully, and the people lived their lives in bounty. But one day, he was nowhere to be seen. His servants found only a single flowery note, written in the tongue of the ancient elementals.THE NOTE:aether :death :aether :entropy :aether :fire :time :light :death :chroma !
:darkness ~ :chroma :earth :light :death :death ~ :aether :entropy :electrum :light :gravity :water ~ :air :fire ~ :time :earth :aether ~ :death :air :fire :life ~ :gravity :air :light :underworld .
:time :earth :aether :chroma :aether ~ :electrum :air :fire :aether :chroma ~ :light :gravity :aether ~ :life :aether :time :time :darkness :fire :life ~ :air :death :underworld :aether :gravity .
:darkness ~ :entropy :darkness :life :earth :time ~ :fire :air :time ~ :electrum :aether ~ :earth :aether :gravity :aether ~ :light :life :light :darkness :fire .
:time :earth :aether :gravity :aether ' :chroma ~ :light ~ :rainbow :aether :gravity :air :rainbow ~ :time :air :air :death ~ :light :chroma ~ :time :earth :aether :gravity :aether ~ :entropy :darkness :life :earth :time ~ :electrum :aether ~ :water :darkness :fire :water :chroma ~ :time :air ~ :electrum :aether ~ :chroma :air :gravity :time :aether :underworld .
:darkness ~ :time :earth :darkness :fire :water ~ :time :earth :aether :gravity :aether ~ :darkness :chroma :fire ' :time ~ :life :air :darkness :fire :life ~ :time :air ~ :electrum :aether ~ :light ~ :entropy :aether :chroma :chroma ~ :entropy :light :underworld :aether ~ :light :chroma ~ :darkness ~ :life :air ~ :air :fire ~ :light :fire :underworld ~ :air :fire , ~ :air :water ?
THE TASKIt is upto you, brave problem solver, to find out what the note says. All you know of the ancient elemental tongue is this: each emoticon corresponds to a single letter of the English alphabet, and ~ refers to the space between words (punctuation is as is in English).
Armed with this information, you must find out what the note says and PM it to the Guildmasters (http://elementscommunity.org/forum/pm/?sa=send;u=7892,7603). You have 1 week.
This is what the note said:
ELEMENTALS!
I SHALL EMBARK ON THE LONG ROAD.
THESE BONES ARE GETTING OLDER.
I MIGHT NOT BE HERE AGAIN.
THERE'S A XEROX TOOL AS THERE MIGHT BE KINKS TO BE SORTED.
I THINK THERE ISN'T GOING TO BE A MESS MADE AS I GO ON AND ON, OK?
Thunderbolts is out due to not sending in a puzzle. So this round might be our finals!
The following message has been decoded by your guild's secret service, (as doing yet another cryptography puzzle is boring), but they cannot find out what the V.T.I.S.S.T.I.H.N.N. PIN code is. Can you?
~WeWereWarriors3 and JustCuteJeans are chatting:~
WeWereWarriors3: Hey...
JustCuteJeans: Hello.
WeWereWarriors3: I had the luckiest match the other day
JustCuteJeans: What happened?
WeWereWarriors3: I was trying out this deck idea in pvp2...
WeWereWarriors3: Creating Singularities, combining them into a chimera, and then freezing and catapulting it...
WeWereWarriors3:
Hover over cards for details, click for permalink
5rp 5rp 5rp 5rp 5rp 5rp 6u3 6u3 6u3 6u3 6u3 6u3 6ve 6ve 6ve 6ve 6ve 6ve 74g 74h 74h 77l 77l 77l 77l 7gn 7q5 7q5 7q5 7q5 8ps
JustCuteJeans: Sounds Risky.
WeWereWarriors3: Everything was going well, but the opponent was using a weird :water- :light duo...
WeWereWarriors3: He played Inundation...
JustCuteJeans: Didn't the Singularities make themselves immaterial?
WeWereWarriors3: They didn't at all during the game...
WeWereWarriors3: They did give themselves a lot of HP though...
WeWereWarriors3: But the opponent also used Shard of Divinity >.<
JustCuteJeans: RIP
WeWereWarriors3: He never used anything on my singularities.
WeWereWarriors3: And my creatures managed to get just enough HP to kill the opponent.
WeWereWarriors3: Next turn, my opponent'd have killed me...
JustCuteJeans: Now thats lucky
WeWereWarriors3: Oh, that's cool... The singularity in slot 1 has twice as much hp as the singularity in slot 2, which has twice as much hp as the singularity in slot 3, etc...
JustCuteJeans: I don't think that works...
WeWereWarriors3: Oops, no, the singularity in slot 1 is 1 hp away from that.
WeWereWarriors3: If you read their HP's from left to right on the field, as if it is a single big number...
WeWereWarriors3: I changed the PIN code of our V.T.I.S.S.T.I.H.N.N. to that.
JustCuteJeans: V.T.I.S.S.T.I.H.N.N.?
WeWereWarriors3: Vault That Is So Secret That It Has No Name.
JustCuteJeans: I have the number. I'll inform the others.
Kakuro (https://en.wikipedia.org/wiki/Kakuro)
(http://imgur.com/gOS0bMm.png)
To send in your solution to the others' puzzle, you have no time left.
OtyUnity has won! BPE concluded that there was no solution to their opponent's puzzle, where in fact there was. Tough luck, BPE.
Solutions:
(http://imgur.com/vWfQykf.png)
or
B | 16\ | 15\ | B | 15\ | 26\ | B |
\12 | 9 | 3 | \16 | 9 | 7 | B |
\9 | 7 | 2 | 12\4 | 1 | 3 | B |
B | \16 | 4 | 6 | 5 | 1 | 5\ |
B | \3 | 1 | 2 | \7 | 6 | 1 |
B | \9 | 5 | 4 | \13 | 9 | 4 |
Solution:
Formula for catapult frozen-damage is: DMG=150*HP/(100+HP), rounded up.
This can be re-written as HP>(100*(DMG-1))/(150-(DMG-1))
We did not define wether there was a mark of :light or not...
So the amount of damage you need could be:
116, 124, 132, ...
this results in your chimera having the following hp, in order:
329, 456, 690, ...
freezing a chimera resets it's hp to 499. Thus, You can only deal 116 or 124 damage.
The 1st Singularity is 1 off of the logic, meaning the logic applies for one (or more) of the following hp's:
328, 330, 455, 457.
It said nowhere that there are 5 singularities; only that there aren't more than 5.
Singularities have relatively to each other this amount of hp, depending on with how many they are:
1: N total: N
2: 2N total: 3N
3: 4N total: 7N
4: 8N total: 15N
5: 16N total: 31N
this means that you have to divide 328, 33, 455, and 457 by this total/N, and get a whole number as result.
You'll find that you can have any of the options with N = 1;
N = 3 can get you 455;
N = 4 can get you 330;
for N = 3, you get on the last creature 455/7 = 65;
on the 3 you'll have 65, 130, 260. the total needs to be 1 higher, so the highest-hp singularity has 1 hp more.
65, 130, 261.
A singularity can only increase it's HP by 5 per turn.
The deck posted only has 4 BB and 30 cards;
this means that there is a maximum of 5+23*5+4*20 = 200 hp on a single singularity.
You'll get the same problem for N = 1.
Thus, only N = 4 for 330 hp is left:
330/15 = 22
hps: 22, 44, 88, 175 <- remember the 1-off thing; for 329 hp you'll need 1 hp less.
Put in the right creature-order on the board.
442217588
Congrats to OytUnity! For your huge achievement, you'll be awarded 50 points! BPE will get 30 points for second place, and Thunderbolts gets 10. Thank you all for bearing with us all these weeks!
Your wording for hard mode was a bit confusing. What you want is an n-column table, where the numbers in top row run from 0 to n-1. The numbers in bottom row can be from 0 to n-1, reflecting the number of times the number above it appears in the bottom row. n is any natural number.
Using i in the table and putting n = imaginary number was confusing, because i refers to the standard imaginary number and those don't interact with normal numbers easily.
There are three solutions if n<7:
For n greater than or equal to 7, a solution is:
0 | 1 | 2 | ... | n-4 | n-3 | n-2 | n-1 |
n-4 | 2 | 1 | 0 | 1 | 0 | 0 | 0 |
Easy to check why, but the how is a bit tough. First, we define the numbers in the bottom row as a(k) where k is the number in the same column above it:
0 | 1 | 2 | ... | n-3 | n-2 | n-1 |
a(0) | a(1) | a(2) | ... | a(n-3) | a(n-2) | a(n-1) |
Now, all the a(k) must add up to n because you only have n numbers in the bottom row (and each of the a(k) is the no. of times k appears on the bottom row). So a(0) + a(1) + a(2) + ... + a(n-2) + a(n-1) = n
Again, because a(k) is the no. of times k appears in the bottom row, you can calculate its sum as the sum of k*a(k) for all k. Therefore, 0*a(0) + 1*a(1) + 2*a(2) + ... + (n-2)*a(n-2) + (n-1)*a(n-1) = n
If you put in the value of n from first equation in second and take all the terms to left side, you get:
(-1)*a(0) + 0*a(1) + 1*a(2) + ... + (n-3)*a(n-2) + (n-2)*a(n-1) = 0
or, 1*a(2) + ... + (n-3)*a(n-2) + (n-2)*a(n-1) = a(0)
Now, let a(0) = X for a solution to the problem. Then a(X) > 0. If a(X) > 1, then (X-1)*a(X) > 2(X-1) > X for all X>2 (and we can prove that X>2 by using the fact that n<7, which can be used to prove that a(n-1), a(n-2) and a(n-3) are all 0).
So, if a(X) = 1, then 1*a(2) + ... + (X-2)*a(X-1) + (X-1)*a(X) + (X)*a(X+1) + ... + (n-3)*a(n-2) + (n-2)*a(n-1) = a(0) leads to:
1*a(2) + ... + (X-2)*a(X-1) + X - 1 + (X)*a(X+1) + ... + (n-3)*a(n-2) + (n-2)*a(n-1) = X
or, 1*a(2) + ... + (X-2)*a(X-1) + (X)*a(X+1) + ... + (n-3)*a(n-2) + (n-2)*a(n-1) = 1
So if any a(k)>0 for k>2 and k=/=X, the left hand side becomes greater than one. So, a(k) = 0 for all k > 2 and k=/=X
or, 1*a(2) + 0 = 1
or, a(2) = 1
Now since a(2) = 1, a(1) > 0. So a(0) is the number of numbers from 3 to n-1, minus 1.
So, X = n-1 - 3 + 1 - 1 = n-4
And so the solution I found before is legit, and it is a unique solution ^^
Edit: Clarified solution for more rigor, thanks Sub for catching my mistake and showing me the other solutions!
What is the starting position?
edit: since you said thats 'as far as you got'
Does a scraper hide equal-height scrapers behind it? derp, this isn't allowed
I'm using A1 as bottom left square, and G1 bottom right.
B6
F3
E2
F5
E5
A5
E4
F6
G7
E6
The rest of the puzzle collapses quickly
A4 == (1,2,3); B4 == (1,2,3,5)
if B4 == 3 => A4 == (1, 2), both of which cause A4, B4, C4, and D4 to be visible from the left.
=> B4 == (1,2,5)
B6 == (1,2,3);
B3 == (1,2);
B2 == (1,5);
B6 is only cell in B that can be 3.
B6 == 3.
F7 == (1,2,3);
F6 == (1,2);
F5 == (2,3,4);
F4 == (1,2,3,5,6);
F3 == (1,2,6);
F2 == (1,4,5);
In F, the '6' is in F3 or F4.
F2 is not visible from the top.
there are only 2 squares in F not visible.
if F3 == (1,2), F3 is not visible from the top;
also, (F3, F6) == (1,2) => F7 == 3 => F6 is not visible from the top.
This'd give 3 non-visible cells; thus, F3 != (1,2)
F3 == 6.
(E3, E6) == (1,2);
E2 == (1,4), but 1 is already used.
E2 == 4.
F5 is the only cell in F that can be '4'.
F5 == 4.
E5 = (1,2,3), but (E3, E6) == (1,2);
E5 == 3.
A5 == 2.
E4 = (1,2,6), but (E3, E6) == (1,2);
E4 == 6.
F2 == (1, 5);
F4 == (1,2,3,5);
if F4 == 5 => F2 == 1 => F6 = 2;
if F4 == (1,2,3), then F4 is not visible because of F5 => F6 must be visible => F6 = 2;
F6 == 2.
G7 is the only cell in the 7-row that can be 2.
G7 == 2.
E6 == 1.
E3 == 2.
B3 == 1.
B2 == 5.
F2 == 1.
F4 is the only cell in F that can be 5.
F4 == 5.
F7 == 3.
A7 == 1.
A4 == 3.
B4 == 2.
G4 == 1.
thats every cell.