Follow-up of the first part and the second part.
Author Archives: chaotic_iak
Introduction to Combinatorial Game Theory, Part 2
Follow-up of the first part.
Introduction to Combinatorial Game Theory, Part 1
I feel the urge to write this post partially because I’m interested on this thing (even though I failed to understand much of the later part of Winning Ways Vol. 1), and partially because I feel bad to begin analysis of The Genius 3’s Monorail with “Sprague-Grundy theorem” without people understanding a thing. Also because I should try writing mathematical posts and stuff. I’m not particularly experienced on this either, so what I’m writing is to the best of my knowledge and might be faulty at points. Blame Wikipedia for not having a good CGT article.
…so let’s go.
Puzzle 91: Margin of Error
Heteromino Divide the white squares into polyominoes of size 3 such that no two identical polyominoes that are also identically oriented are orthogonally adjacent.
Expected difficulty Hard • Answer • Comment/E-mail if you want a solution to be published
Puzzle 91: Margin of Error
Heteromino
Oh yay I’m alive.
There we go. Recently I got the inspiration of Heteromino with a two-cell wide empty border. A 10×10 doesn’t seem to work, since I only have 6×6 space to work with the black cells, but a 14×14 looks good. Besides, I can say “here’s the 10×10 puzzle, and in case you need it, here’s two-cell margin of error around the grid if you’re stuck or something”.
…yes, I appear to be terribly uninspired for titling puzzles.
Also, I appear to start playing Pokémon Trading Card Game Online. It’s free to play, although getting the in-game currency to get more cards might be a little hard.
The Genius, by A Skymin’s Mind #7
Monorail
Used as Death Match of Season 3, Round 10 and Season 4, Round 6. (Discussion of S4E6 in particular will come later.)
Rules
The objective is to be the one that completes a train track, or to be the one that declares it’s impossible (correctly).
There are 18 square tiles used in the game. Two of them show straight tracks, the station tiles, which are already placed on the grid; the remaining 16 tiles can be made to show a straight track or a bend track, which are to be placed. Players place tiles so that sides match (a track leading to a non-track side is not permitted; think of tile-based games (such as Dominoes or Carcassonne, where sides of tiles must match). A player may place one to three tiles at once, but all of them must be played in a straight line contiguously (think of Scrabble, where you cannot place your tiles separated, only that it’s even more strict; the tiles must be contiguous, not separated by already existing tiles). However, the track itself doesn’t need to be connected; as long as the tiles placed are connected, it’s fine.
The person who places the last tile, completing the track using all tiles already placed, wins. However, a player can also declare that it’s impossible to complete the track, in which the opponent must either complete it (for a win to the non-challenger) or resign (for a win to the challenger).
Also see this video from the Facebook page, which is unfortunately in Korean, but gives illustrations.
So it’s my birthday.
And I don’t have anything to post, anything to say… I haven’t created any puzzle to post here for several weeks. I registered on FurryMUCK, which adds something to the list of things to waste my time, and I mostly spend time browsing the net or playing SpaceChem. (On the good news, SpaceChem cleared! Except three more optional levels, which I’ll catch up some time.)
I don’t know why I procrastinate so badly… But happy birthday to myself, yay.
The Genius, by A Skymin’s Mind #6
Open, Pass
Used as Main Match of Season 1, Round 7.
Rules
Each player receives a deck of 20 cards, numbered 0-9 along with mathematical operations +, -, ×, ÷. They may spend garnets to buy additional cards from three decks: black, red, and blue, worth 1, 2, 3 garnets each, and have increasingly better cards. (For example, the black number cards are two copies of 0-3 and one copy of 7-8, while the blue number cards are three copies of 7-9 and one copy of 10. Also, black operation cards have three of subtraction and division, with two of the others, while blue operation cards invert this, having three additions and multiplications and two of the others.)
After buying cards and exchanging with other players if necessary, each player constructs a 20-card deck, which will be shuffled by the dealer. A player may ask for a reshuffle for at most three times. After a player is satisfied with their lay, the dealer begins filling a 10-slot expression with the deck. Each time, a card is placed face down at the rightmost empty space. The player may choose either to open the card, thus opening it and fixing its position, or pass the card, throwing it away without seeing its value. After ten opens (and thus at most ten passes), the expression is created. Only the leftmost number is kept across a stretch of numbers, and similarly with operations. After that, if the rightmost card in the expression is an operation, it is discarded, and if the leftmost card is an operation, a zero is appended to the left of the expression. The result is then evaluated and becomes the score. For example, -, 8, 5, 7, +, ×, 3, ÷, 5, + is converted into 0 – 8 + 3 ÷ 5 = -7.4. The winner is the person with the highest score.
Protected: Potentially sensitive content; guess the password!
Touhou Project
A danmaku (bullet hell) game series, produced by a single person for the last 20 years or so, that I’m currently playing a lot. So what is bullet hell? Well, here’s one image.
Partyyyyy
Yes, those are bullets, and you’re supposed to dodge them as you shoot to attack the boss.
The fact that I enjoy this game series immensely despite not liking shooting games in general might be because of my interest on difficult games. (Games whose genre includes “hell” in it should be hard…) And yes, I also like difficult games like Super Hexagon, oO, and such kind of games. (I also like puzzle games, but seeing that most puzzle games have no such difficult replayable sections, I like them for a different reason.)
How many of my little readerbase (if that’s a word) know this game?
The Genius, by A Skymin’s Mind #5
Truth Detector
Used as Season 2 Final Game, Round 2.
Rules
There are two players. Each player prepares a 4-digit password and tries to hide it from his opponent. Then each player, in turn, can start asking questions to each other, which must be answered untruthfully. In other words, if you ask “How many times the digit 0 appears in your code?” and you receive a reply of 0, it means there exists the digit 0 in the code (because the reply is wrong). However, this reply cannot be an impossible reply (such as an answer of “5” for the above, considering that there are only 4 digits) or an unrelated/evasive reply (such as “I don’t know”). Additionally, questions must only be about the password. When giving a truth or any of the forbidden replies above, the penalty is revealing a digit not in the password.
When one thinks he knows the password of the other, he may use the turn to answer instead, guessing the password. If this is correct, he is the winner; if this is incorrect, the turn passes to the opponent.
As this is a Final Game, there are three items given:
- Starting Player: The person with this item may start asking question first.
- Truth Penalty Exemption: If a person accidentally answers the truth, using this item he may avoid the penalty once.
- Double Turn: This item may be used to give an additional turn, be it for asking or guessing.
Chaos at the Sky 
