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43 votes
Accepted

Any fans of The Big Bang Theory?

The key to solving this question is noticing This is a hint to what the dartboard actually represents: So the scoring is given by
Deusovi's user avatar
  • 146k
40 votes
Accepted

Winning chance in coins game with fixing

GoblinGuide's user avatar
24 votes
Accepted

Two-Move Chess Game

fblundun's user avatar
  • 1,536
16 votes

Making a 2n-digit number divisible by 9

I believe that Bob can win if (and only if) n is
SQLnoob's user avatar
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12 votes
Accepted

Game of the glasses on the windowsill

Here is my evaluation: Conclusion And yet...
Florian F's user avatar
  • 30k
11 votes

Making a 2n-digit number divisible by 9

I'll add on to SQLnoob's answer and say Bob can't win if n isn't So she chooses $$ m = \begin{cases} 7-k & k < 7 \\ 1 & k = 7, 8 \end{cases} $$ For example,
Tyler Seacrest's user avatar
8 votes

Any fans of The Big Bang Theory?

Howard's last dart doesn't land since he's realised that he's dreaming, given that lighting a fire indoors would be a breach of the Pasadena ordinance prohibiting the lighting of an uncontrolled fire ...
Richard's user avatar
  • 5,330
8 votes
Accepted

The game of 42: 10 cards to make 42

wins by Examples:
Albert.Lang's user avatar
  • 5,652
7 votes

The Kyiv Triangle Game

Alice has a winning strategy.
Sunny Lu's user avatar
  • 3,290
6 votes

Bigger number (sometimes) wins

Here is the phase diagram for the game, with player X being red and player Y being blue. Solid lines and shaded regions indicate that the respective player wins. The solid black line indicates a draw. ...
DanDan面's user avatar
  • 711
6 votes

Winning chance in coins game with fixing

This is not nearly as elegant as GoblinGuide's simple answer: https://puzzling.stackexchange.com/a/126192/1777 The probability of winning is always: Strategy: For any given N coins, there is: This ...
LeppyR64's user avatar
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5 votes
Accepted

The Kyiv Triangle Game

I only attempt to answer the puzzle by assuming that "triangle" means "small triangle". I started thinking about the problem before understanding how the others could see $27$ ...
Plop's user avatar
  • 206
5 votes
Accepted

Don't let 'em die!

Two weak bounds which can surely be improved. The hero can save at most Here's the villain's strategy to kill the rest: On the other hand, the hero can save at least by
xnor's user avatar
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4 votes
Accepted

Bigger number (sometimes) wins

Assuming the opponent has access to our strategy beforehand and we want to provide a way to still ensure even odds, my first attempt was So instead, I tried generalizing: So the final strategy is: ...
PattuX's user avatar
  • 552
4 votes

One vs many. Can white force a draw?

In figures (1a), (1b), (2a), and (2b), the white cells are empty and the red cells may or may not contain black pieces. The pattern continues in the obvious way out to the infinities. In figures (3a)...
geometrian's user avatar
4 votes

A question from Bob to Bob

Nuclear Hoagie's user avatar
3 votes

The game of 42: 10 cards to make 42

In complement to the very neat answer by Albert, I wanted to show the graph of the game (open in a separate tab, it is big): A state of the game is defined by the cards in stack 2, and is represented ...
Fluorine's user avatar
  • 547
3 votes

Pursuit-evasion game

First of all, how can the criminal even get caught? Can the cops arrange this scenario? How long does this take?
AxiomaticSystem's user avatar
2 votes

Pokemon battle puzzle: Chansey vs Wobbuffet

One detail that was missing from the question is what abilities both Pokémon have. Assuming standard abilities (i.e., Shadow Tag for Wobbuffet and Natural Cure or Serene Grace for Chansey), these do ...
PattuX's user avatar
  • 552
2 votes

One vs many. Can white force a draw?

Partial answer for N=4
Retudin's user avatar
  • 8,977
2 votes

A question from Bob to Bob

Brief: Day 1: Bob shares with John a question about day 2 of a fact that John can physically control. John leaves the room. Day 2: Nothing/Something happens. Day 3: John enters the room. John read ...
10010100102ohno's user avatar
2 votes

Press The Grue Button

The fastest way to achieve success is:
Nuclear Hoagie's user avatar
1 vote

The Kyiv Triangle Game

I've played several games of this and found that, in my random assignments, Alice tends to win. While I haven't proven that this is the winning strategy, I have found a strategy that I have yet to ...
Truej's user avatar
  • 532
1 vote

Prime Boggle Game

EDIT: I missed the requirement that primes must be unique. That invalidates this first grid. But the final solution should still be fine. The longest game I can find comprises 39 moves. This is ...
GentlePurpleRain's user avatar
1 vote

Press The Grue Button

The strategy that each worker adheres to:
Pumbaa's user avatar
  • 938
1 vote

A question from Bob to Bob

How about:
fblundun's user avatar
  • 1,536
1 vote

A question from Bob to Bob

Ed Murphy's user avatar
  • 2,102
1 vote
Accepted

Zigzag nim game

As you suspected, the correct approach is to start from the end. First, let's invent a notation for the game positions. Let's view each position from the POV of the player whose turn it is, so that &...
Bass's user avatar
  • 77.4k

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