# Two real numbers

Initially found from xkcd’s blog, then got a link to MathOverflow.

Suppose you are playing a game with Alice. She uses some probability distribution to pick two distinct real numbers and writes them in two envelopes. You then choose either of the envelope and opens the number inside the envelope. Is there a strategy that guarantees you a strictly larger than 50% probability to guess correctly whether the chosen real number is the greater or the lesser, for any probability distribution that Alice uses?

This is my take on the problem; feel free to comment, discuss, or argue with me! As long as the discussion is kept civil.

# NP-Complete Games and Puzzles

I love puzzles so much. I also plan to go for computer science. Of course this had to be done. Here’s a list of everything I’ve found. This post will (hopefully) be updated every time I get a new thing. Contributions welcome.

My target: Prove or disprove that Yajilin is NP-complete. :v

Last updated 16-Nov-2013

Puzzles that are proven NP-complete by reductions from…

3-colorability of planar graphs Corral

3-partition Tetris Survival

Bin packing Battleships

Existence of Hamiltonian circuit in cubic planar graphs Masyu, Slitherlink

Latin square Sudoku

Nondeterministic Constraint Logic Nonogram

# Puzzle 72: Drunk Man

Short Yajilin Follow regular Yajilin rules: This is loop style puzzle. The loop may not pass through any gray cell. White cells not passed by the loop may not be orthogonally adjacent; note that a white cell not passed by the loop may still be orthogonally adjacent to a gray cell. A number with an arrow indicates the number of cells not passed by the loop, looking from the cell with the number in the arrow’s direction, up to the edge of the grid.

In addition, no straight segment of the loop may be more than two units long. In other words, whenever the loop goes straight through a cell, it must turn both before and after it.

Expected difficulty Medium-hardAnswerComment/E-mail if you want a solution to be published

Puzzle 72: Drunk Man
Short Yajilin

Re title: Originally I wanted to give the variation name “Drunk Yajilin”, but that’s too weird. And well, drunk people can’t walk straight for long, or so the “usual” “sources” say.

Re difficulty: I consider hard. Prasanna says medium, close to hard. So let’s make it medium because Prasanna is more skilled and less biased (any author will be biased to their own works) than me.

Well… Not much comment, actually. My birthday is coming. All my puzzle projects (Fillomino crazy variants batch, Fillomino Variations pack, perhaps more that I don’t remember) are abandoned except for the upcoming LMI test in early 2014. Probably February, but not confirmed yet. I have homework and I make puzzles…

# Special Puzzle 12: Too Hard to Guess My Mind

Mysterious Rules Given the initial puzzle state and the solution, deduce a probable set of rules.

Special Puzzle 12: Too Hard to Guess My Mind
Mysterious Rules

Solution
- Open room B, then close it.
- Open rooms C and E, then close E and C.
- Open rooms B, D, F, then close D and B.
- Open rooms C, E, pass through F, and open G.

Rules (aka answer to the puzzle)

You start from the topmost room. Reach the bottommost room.

In each room, there are two numbers; the cost (in gems) to enter the room and the number of gems inside the room, in that order. (For example, 4/2 means a cost of 4 gems to enter and you get 2 gems upon entering.)

Gems inside the room don’t regenerate; once you take them, they won’t appear again when you come again.

You can close (lock) a room and gain 50% refund. (For example, a room with a cost of 4 gems will refund you 2 gems when you lock it.) You can leave a room without locking it, if you wish.

A room can only be unlocked from the top, and upon locking a room, you must go to a higher room.

So… I’m bored. Here’s the result of my bored mind. I should return to making pencil puzzles…

# Midterm

Midterm. The word that many people hate. A week full of study and pressure. In most colleges, midterm counts at about 25-50% of the final score, with finals counting about 40-60% and the rest are attendance/homework/quiz/etc. Failing midterm means a maximum of about B, or C if you’re unlucky enough to hit the 50% midterm course…

The midterm for me is next week, 21-25 October. Although due to my choices of courses or probably just luck, I have no midterm on the last two days, giving a nice half-week holiday :3

What will I do to prepare for the midterm?

I won’t do much, actually. I’ll just learn a little bit more than usual tests at school or quizzes here. Looking back from my quizzes, I studied for a total of zero seconds for Calculus I, also zero seconds for Biology, another zero seconds for Introduction to Programming, yet another zero seconds for Basic Korean I (which now I regret), and probably about 20 minutes for each Chemistry quiz. There’s no quiz for Physics yet, and heck, there’s no midterm for Physics. So, I plan to approximately do…

- 20 minutes of study for Calculus I, mostly to review what the definitions are.
- An hour for Biology, mostly to reminding self what things are different from what learned at school.
- 20 minutes for Introduction to Programming, mostly to toy with Python’s quirks.
- An unknown amount of time (probably 3-4 hours in total) for Basic Korean I, because I can’t do languages.
- An unknown amount of time (probably 2-3 hours in total) for Chemistry, because what the heck is Schrodinger’s equation doing in chemistry?!

I mostly plan to get enough sleep though. Even though the exams are at the end of the days (none is before 16.00, and on all days I’ll stay until 22.00), a good sleep is still good. Compare with the scenario of not enough sleep, where I might oversleep and rush to prepare myself to get to the exams…

…oh dammit it’s 25.00 here already. For the uninformed, 25.00 means 01.00 on the next day. I start to keep the time rolling continuously, only subtracting 24 hours (and advancing the day by one) every time I sleep for considerable time.

Ugh anyway. Homework…

# Puzzle 71: Checkerboard Insanity

Tapa Region Party Follow regular Tapa rules: Do Nurikabe-style. (The black cells are called the Tapa wall.) Cells with numbers may not be black. Numbers in a cell indicate the sizes of the black square groups adjacent to the clue square; two separate black square groups must be separated by at least one white square.

In addition, Region Party variation apples. The two quadrants with blue cells and “C” at the top-left of the cells indicate Clones quadrants: The contents of the two quadrants must be identical on the blue cells. (There is no restriction for cells inside the quadrants that are not blue.) The two quadrants with red cells and “E” at the top-right of the cells indicate Extra Region. After tilting the grid by 45 degrees, the blackened cells on the red squares also form a Tapa wall. (Note that all red squares form a single region, not two separate regions.)

Expected difficulty HardAnswerComment/E-mail if you want a solution to be published

Puzzle 71: Checkerboard Insanity
Tapa Region Party

Perhaps the only puzzle among the most recent 20 or so that is made purely on computer, not using my puzzle scratch book. The difficulty is hard; I wanted to go with medium but the variant is pretty confusing on itself.

Anyway. What inspired me? The recent TVCs and CTC on LMI, of course. Plus me recalling that I’ve done this crazy variant before. :3

And…uh…this variant is hard >_< The best finish I’ve found is unsatisfactory. But fair enough for a puzzle I make in half hour or so.

I need to make some easy puzzles for my “mate”… Ideas?

# Puzzle 70: Mii~ >w<

Greater Than Fillomino Follow regular Fillomino rules. In addition, inequality signs appear on the grid; these signs must be satisfied by the numbers in the squares involved.

Expected difficulty HardAnswerComment/E-mail if you want a solution to be published

Puzzle 70: Mii~ >w<
Greater Than Fillomino
(Here for plain version)

So, as a “natural” follow-up of my current interest on roleplaying, this is obligatory. All givens form either the emoticon ^^ or <3. I wanted to include =3 (equals sign and 3, effectively two horizontally adjacent 3′s) but if I can use only two emoticons why not. I didn’t want to figure out what happens with only one emoticon though, this by itself is already difficult to construct…

Hard, yeah. Because a few parts are hard. But if I’d use the average, this would be somewhere around medium, because the easy parts are easy. And the puzzle breaks down nicely into parts. *insert obligatory reference to vore*

So! This puzzle is a gift for an RP friend that is curious about puzzles. He solved Puzzle 1, a puzzle I believe to be “final test to see whether you advance from beginner to intermediate Fillomino solver”. Even though he clocked 2 hours, this is a fabulous achievement for someone with no prior experience of logic puzzles. And so I felt really guilty when testsolving the puzzle; I found the puzzle to have the mentioned hard steps. There are even parts where my best method is still trial and error to some extent (read: “what-if”s), but hey. Who cares about time. Let’s see whether the aforementioned RP friend can solve this :3

And finally, yeah. Mii~ >w<