Skip to main content
60 votes
Accepted

Rock, Paper, Scissors and Trump

Looks like One strategy would be to The opponent will naturally soon realise what's happening. But it won't help. Here are the possible results from Alicia's point of view: So whatever the ...
Bass's user avatar
  • 77.9k
42 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
  • 148k
40 votes
Accepted

Winning chance in coins game with fixing

GoblinGuide's user avatar
37 votes
Accepted

Making a 9 digit number divisible by 11

Note: This answer assumes that the non-zero restriction only holds for the first move, not for any subsequent digits, i.e. that the restriction was imposed only to ensure a valid 9-digit number was ...
Jaap Scherphuis's user avatar
30 votes

Finding digits that sum to 15

The solution: The reason:
Deusovi's user avatar
  • 148k
27 votes
Accepted

Who would be the first to defeat an abundant number?

Daniel Mathias's user avatar
26 votes
Accepted

Polynomial game with Devil

It is always possible for you to force the polynomial to have the root $-2$: $$ x^2 + (a+2) x + 2a = (x+2)(x+a)$$ Your strategy is to increase your term until it is slightly higher than half the ...
user3294068's user avatar
  • 7,518
26 votes

A Tic-Tac-Toe type game

Another strategy for that works for any odd number of squares:
ffao's user avatar
  • 21.8k
25 votes
Accepted

Two-Move Chess Game

fblundun's user avatar
  • 1,704
21 votes
Accepted

It'd be on an infinite board, but he can't fit one in his hideout

The winning strategy is and in fact,
Deusovi's user avatar
  • 148k
20 votes

The 100 soldier problem

I'll kick off with some observations. Determining a Nash Equilibrium for such a large solution space is not trivial. So here are some numerical attempts for much simpler problems: For problem a, it ...
Dr Xorile's user avatar
  • 23.7k
19 votes
Accepted

99 numbers on the blackboard

I believe this is the answer. The strategy is below. Edit: Slightly clearer response with strategy.
cmxu's user avatar
  • 1,016
19 votes
Accepted

Noughts and Crosses puzzle

The position is as follows: No two of Eques's counters occupy the same line of 3 (satisfying the never-threatening requirement), and no matter where Knott (O) places their next O, Eques (X) has a ...
Stiv's user avatar
  • 146k
19 votes
Accepted

Blindfold Tic-Tac-Toe

You can't do this going second: The strategy going first is: Interestingly,
Deusovi's user avatar
  • 148k
19 votes
Accepted

Catching a Cat on an infinite Line

This is a (semi)infinite version of the Princess in the Castle problem, which is also often asked using a fox or bunny in a row of holes. Infinite is hard to deal with, so lets make it somewhat finite ...
Jaap Scherphuis's user avatar
16 votes

Rubik's cube two-person game

Answer: Reasoning:
xnor's user avatar
  • 27.4k
16 votes
Accepted

A Tic-Tac-Toe type game

I think the answer is that the Strategy
hexomino's user avatar
  • 138k
16 votes
Accepted

Fight Battle 21

I'd Then Then So
SteveV's user avatar
  • 15.9k
16 votes
Accepted

Reverse dots and boxes

I would suggest an alternate (simpler) strategy:
Smock's user avatar
  • 950
16 votes
Accepted

Masyu-making game

Up to symmetries of the board, there aren't very many possible moves for the first player: Does this strategy work?
Deusovi's user avatar
  • 148k
16 votes

The Game of Barranca

I'll address whether values of N exist such that if the target of the game is N, there is a winning strategy for the second player[.] The answer is First, a lemma: This seems straightforward ...
msh210's user avatar
  • 12.9k
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
  • 8,590
15 votes

Clear board in Othello (Generalisation)

Here is one way you could begin to prove that the board can be cleared for all values of $m$ and $n$. Proof by induction. [incomplete] Case 1: $k = 1$ Here we take k = 1 to mean the smallest ...
Tim's user avatar
  • 1,018
15 votes

25 square puzzle

Here is another simpler proof This generalises to all odd n. For even n, however, ...
Jaap Scherphuis's user avatar
15 votes

Spider and fly on a cube

I think Oray got the right answer. Here are some drawings to illustrate the solution.
Jaap Scherphuis's user avatar
15 votes
Accepted

Can you survive this infinite zombie attack?

Answer: Strategy: Visualisation: Proof:
loopy walt's user avatar
  • 21.3k
15 votes

Who wins this game?

How about this: This method works for $n > 2^k$.
ralphmerridew's user avatar
14 votes
Accepted

A search game with 2016 numbers

It can be done in: For our questions we use questions similar to those from Ivo Becker's answer: Proof:
A Smith's user avatar
  • 156
14 votes
Accepted

A Tic-Tac-Toe variant with three marks - winning strategy and chances

Solution Step-by-step deduction If A plays first, then Proof: the crucial realisation is that B can always force A to play in a specific square. WLOG, say A's first move is an $X$. If A's first ...
Rand al'Thor's user avatar

Only top scored, non community-wiki answers of a minimum length are eligible