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40 votes
Accepted

Winning chance in coins game with fixing

GoblinGuide's user avatar
30 votes
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Find the heaviest and the second heaviest coins

fljx's user avatar
  • 16.6k
29 votes
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Can you beat random?

Here's how you win in the long run Expected number of losses Thanks to Evargalo for fixing the last calculation.
hexomino's user avatar
  • 137k
27 votes

Sliding crosses in a 5x5 grid

I saw these questions late, so I decided to answer all 3 (3x3, 4x4, 5x5 grids) as well as the general case (nxn grids). The answer is
Bryce's user avatar
  • 559
22 votes
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Sliding crosses in a 5x5 grid

The answer is (maybe surprisingly) Lets reverse engineer the problem: So we can do so by doing the following:
Beastly Gerbil's user avatar
21 votes
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Two prisoners and twenty marbles

Same number of nights as in PDT's solution but perhaps expressed in a simpler way.
Florian F's user avatar
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20 votes

Can you beat random?

I agree with both answers, but the answer is a little simpler than their explanations. It can be simplified to: Those two rules alone cover every possibility. For completeness:
Stevish's user avatar
  • 1,345
19 votes
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Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

NoeS's user avatar
  • 279
18 votes
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Poison ivy chess: Can the king get to safety?

The king can get to safety via this simple strategy: Look upon the squares on the main diagonal. Think of each square as a jumping target. (Image: Light gray squares represent the position of the ...
new Q Open Wid's user avatar
18 votes
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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
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Magic: the Gathering – Scry-sort

Assume the N cards are labeled with their desired order, 1 through N. Compare the top two cards and place the smaller of the two on the bottom. Repeat step 1 (N − 1) times. Move the top card to the ...
2012rcampion's user avatar
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13 votes

Determine whether the counterfeit coin is heavier or lighter in two weighings on a standard balance

Goldstein's user avatar
  • 291
12 votes
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Game of the glasses on the windowsill

Here is my evaluation: Conclusion And yet...
Florian F's user avatar
  • 30.6k
12 votes
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Anna tries to make triangles from broken sticks

In fact
Ross Millikan's user avatar
11 votes
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Sliding crosses in a 4x4 grid

Is one cross possible? Multiple crosses?
fljx's user avatar
  • 16.6k
11 votes

Two prisoners and twenty marbles

They can do it in 10 nights at least:
PDT's user avatar
  • 15.3k
11 votes

Keys and Locks Puzzle

I believe the condition is: This condition is sufficient. Is this condition necessary?
Florian F's user avatar
  • 30.6k
10 votes

Can you beat random?

Here is a winning strategy: Then at each move there are 3 possibilities: Your expected win is Your probabilities for round n (n>1) are: Counting 1 for a win, 1/2 for a draw and 0 for a loss, ...
Evargalo's user avatar
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10 votes
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More Catching of Cats

Let's summarize Jaap Scherphuis's answer to the easier version of the problem where the cat can only move 1 step at a time: Now, since in this version the cat has a step size of $k$, we have to ...
Carmeister's user avatar
  • 2,547
8 votes
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Sliding crosses in a 3x3 grid

Consider
Daniel S's user avatar
  • 6,959
8 votes

Seven genuine and two fake coins

Here is a method. Let's name the coins ABC DEF GHI.
Florian F's user avatar
  • 30.6k
8 votes
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Making an expression with the numbers 1 to 100 odd (or even)

On her first move, Anna can Anna's subsequent moves depend on Boris' subsequent moves. This works because
kyle's user avatar
  • 218
8 votes

Is it possible to fill an arbitrarily large hex grid completely given these rules?

I claim that the answer is and here's why:
Deusovi's user avatar
  • 147k
8 votes
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Is it possible to fill an arbitrarily large hex grid completely given these rules? #2

I claim the answer is because
Deusovi's user avatar
  • 147k
8 votes
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The game of 42: 10 cards to make 42

wins by Examples:
Albert.Lang's user avatar
  • 6,185
8 votes

Catching a Cat on an infinite Line

Nobody has yet answered the final question, which is the most interesting part... The cat can circumvent capture on any graph with a doubly-infinite chain or a cycle of length at least 3 or size-3 ...
user21820's user avatar
  • 1,236
7 votes
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Minimum K for detecting fake pearls in one weighing

As others have shown, it suffices to find a $10$-set whose $2^{10}$ subsets have distinct sums, and we want to minimize the maximum element of this $10$-set. An upper bound from https://oeis.org/...
RobPratt's user avatar
  • 14k
7 votes
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A game of 101 stones—win at (not quite) all costs

Time for an answer to the bonus question! We'll go straight to the generalized case. The theorem we shall prove is: We have chosen to assume that $N$ is odd, since if $N$ is even, it introduces the ...
Arcorann's user avatar
  • 186
7 votes
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Gold and silver coins in sealed envelopes

I feel like someone should discuss the axiom of choice in an answer. Bob's strategy First, let's consider a modified puzzle where Alice only has a finite number of gold coins. Here's a strategy Bob ...
tehtmi's user avatar
  • 3,326
7 votes
Accepted

Two Trains, One Track

Not sure if it's optimal, but here's a solution: Note that the same number of steps would work with larger trains:
Kris Van Bael's user avatar

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