Puzzle 90: Antimatter

Dual Masyu Follow regular Masyu rules. This is a loop puzzle: Draw a loop that passes some of the cells such that the loop never touches or crosses itself, the loop only turns on cell centers, and the loop only makes 90-degree turns. The loop must pass all circles. When it passes a white circle, it must go straight, but must turn either before or after (or both). When it passes a black circle, it must turn, but must go straight both before and after it.

Additionally, this puzzle is two in one; it has two solutions that are coupled in the following way. Gray circles are two circles that have different colors in the two puzzles; if a gray circle acts as a white circle in one puzzle, then it must be black in the other, and vice versa. (In either puzzle, two gray circles may act as one white and one black; they don’t need to act as the same color.)

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

Puzzle 90: Dual Masyu

Puzzle 90: Antimatter
Dual Masyu

No particular comment; just toying with interesting things.

The Genius, by A Skymin’s Mind #4

Scamming Horse Race

Used as Main Match of Season 1, Round 5, and inspires Main Match of Season 1, Round 10, for a later issue.

Rules

There is a horse race involving eight horses, traveling across 20 spaces. There are 12 rounds; in each round, each horse advances by a predetermined amount between 0 and 3 spaces, inclusive. (The result of the race is already determined.) Players should bet on which horses will finish first or second; there are no distinction on whether they bet on the horse placing first or the horse placing second.

Players have 20 chips at the beginning, and they may bet at most three chips after each round. They may not bet on horses in no-bet zone, the last four spaces of the race. Unused chips are discarded, and correct bets receive payoffs depending on their odds; the less chips bet on a horse, the larger the payoff per chip will be.

Each player has received a hint at the beginning of the game, and they may also look at any of three additional hints by paying three garnets for each hint.

Chips not wagered on any horse are lost at the end. The player with the biggest payout wins, and the smallest payout loses.

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A/B + C/D

I was contacted by a friend that maintains an online judge, asking about the solution to a particular problem that has existed for how many days on an “easy” section.

Basically, the problem is this: given positive integers A, B, C, D, compute A/B + C/D and simplify it. You are guaranteed that if you represent A/B + C/D = E/F in lowest terms, then all of A,B,C,D,E,F fit in p-bit integers (in the problem, p = 64). Your task is to find this E and F.

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The Genius, by A Skymin’s Mind #3

Tactical Yutnori

Used as Death Match of Season 1, Rounds 3, 4, 10.

Rules

Basic yutnori rules apply, as follows. Wikipedia is also pretty complete.

The game uses a special yutnori board. Players cast yut sticks which can be “up” (plain) or “down” (marked). There are thus four sticks cast. The number of up sticks is the player’s score: one up stick is 도 (do), scoring one space; two up sticks is 개 (gae), scoring two spaces; three up sticks is 걸 (geol), scoring three spaces; four up sticks is 윷 (yut), scoring four spaces; and no up sticks is 모 (mo), scoring five spaces, unlike the others. In addition, yut and mo also allow the player to cast again, thus possibly accumulating several yuts and mos before a different cast is thrown.

Each player has two pieces on the board. After a move, the player can move any of their pieces for the score cast. In case of yuts and mos, they can choose where each cast goes to, but a cast can be only used for one piece. (For example, with a yut and a gae, one can use them to advance a piece six spaces (4+2) or a piece four spaces and another two spaces, but not split them into three and three.)

Normally, pieces travel along the outer edge of the board. However, when a piece lands on a corner or the center of the board, it has the option of following a different, shorter route. Note that the piece must land on the corner or the center to allow the alternative route; simply passing by doesn’t count.

When a piece lands on another of its own, the two may decide to merge and continue together. When a piece lands on an opponent’s, the opponent piece is returned back to home and the player gets another cast. (It seems that if one gets a yut or a mo in this new cast, it doesn’t give another cast.) A player wins if they get both pieces back to the home after circling the board.

That concludes yutnori rules. However, as this is a tactical yutnori, additional rules are in place.

The two Death Match players each chooses a partner. The partners also play, but they cannot win. Each player holds two sticks, one is “up” on both sides and one is “down” on both sides, and each throws one stick of their choice. (Teammates may discuss, of course.)

In addition, there is a variant called “back do”. If one gets a do, instead of advancing by one space, a piece is retracted by one space. (If one doesn’t have any piece on the board, the turn is skipped.) Note that this allows a piece to retract back to home and beyond by back dos, and it’s still counted as circling the board.

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The Genius, by A Skymin’s Mind #2

See here for explanation of this series.

Winning Streak

Used as Death Match of Season 1, Rounds 1, 2, 5.

Rules

Two people, the Death Match players, are playing rock-paper-scissors against all other people in a randomized order. Plays can only result on a win or a loss; in case of a tie, the play is repeated. After each player has played against all other people, the longest streak of wins is scored; the one with longer streak wins. (As there has never been any tie, it’s not known what happens on a tie, but I guess the next longest streak is compared, and so on, replaying the game if the whole thing is a tie.)

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The Genius, by A Skymin’s Mind #1

A Korean game show, which I watched online (subtitled of course, so go watch it too) from here. Basically all players play a game, called the Main Match. The loser, called the Elimination Candidate, can choose another person to join them in the Death Match, where one player is eliminated. (In case of multiple losers, the winners choose the one to be Elimination Candidate among them, and they later choose again the opponent as usual.) Rinse and repeat with different games.

So here I just want to talk about the games and my strategy for some of them. Note that this might be a light spoiler for everything, because I don’t list the games in order, so go watch all of them first before reading I suppose. This will be a series that will run for who knows how long.

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