# Special Puzzles 2-4: Not Your Usual Logic Puzzles

Not your usual logic puzzles. For proof, see Special Puzzle 1 (no pun intended).

To be taken as very short (read: 10 seconds or so) (hopefully-)fun diversions when solving ridiculously tough puzzles. They are all ridiculously easy for that reason…maybe.

Also, I have prepared all the way to Puzzle 21. They will appear at 12 hours from another, so Puzzle 18 will be 12 hours from now and Puzzle 21 will be 48 hours from now. Puzzle 18 is a KenKen.

Special Puzzle 2: Cipher Skyscrapers [Single]

Cipher Skyscrapers. Each identical letter represents the same digit and each different letter represents different digits…wait there’s only one letter here. Put a number between 1 and the length of a side of the grid such that each number appears exactly once in each row and column. If the numbers represent heights of buildings, the numbers outside the grid tell the number of visible buildings from that point looking into the grid, with higher buildings block lower ones in visibility.

There might be multiple solutions, however in all these solutions the gray cell’s content is equal. What’s the number in it? Your answer should be in {1,2,3}.

Special Puzzle 2: Cipher Skyscrapers [Single]

For a slightly more difficult (read: from ridiculously easy to still-ridiculously easy) version, try to identify the digit above the gray cell. Yep, the number of buildings the observer from the top of the second column can see.

Special Puzzle 3: Cipher Skyscrapers [Correct Given]

Cipher Skyscrapers as above. Although there might be multiple solutions, there is only one value of the cell with the question mark that will give a single solution has that cell be a given. What’s that value? Your answer should be in {1,2,3}.

This is the same puzzle presented in four ways. Which one do you think is the easiest to solve?

Special Puzzle 3 (a-d): Cipher Skyscrapers [Correct Given]

Can you find a puzzle (not necessarily Skyscrapers) with as many possible solutions as you can where you can specify any one square as a given (substituting it with a correct value) to make the solution unique? In the above puzzle, I have 7 solutions, but only 4 cells out of the 9 cells can make the solution unique (the other 5 can’t).

Special Puzzle 4: Invertible Hidato [Count the Solutions]

Hidato. Put a number between 1 and the number of white squares in the grid such that every two consecutive numbers share a vertex (or an edge; that’s also sharing a vertex right?).

Fill the numbers in the invertible style (this year’s USPC’s Math Flip or this style of numbers), since the Hidato must also form a valid Hidato when the grid is rotated upside down. How numbers pair up is written below the grid; single numbers when rotated form themselves.

I know that there are multiple solutions. Your task is not to find them; not indirectly anyway. Your task is to find the number of solutions.

Special Puzzle 4: Invertible Hidato [Count the Solutions]

Extra task: Prove that there is no invertible Hidato for a 3×3 grid. (The numbers are 1-9 obviously.)

I hope you find these diversion puzzles fun…and maybe inspire you to make a “full-scale” puzzles of these abnormal variations. Well, Single has been done before, Correct Given is unique to this puzzle but I think people won’t like it, and Count the Solutions is pretty obviously a downgraded form of Correct Given. I’ll doing Single sometime in the future then…not in the foreseeable future.