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1500 questions
28
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7 answers

Simulating an unbiased coin with a biased one

You are given a biased coin. With probability $p$ it produces heads, where $p$ is in the range $(0,1)$. How can you use this coin to simulate an unbiased fair coin, ie., a coin that produces heads with probability $0.5$?
Dmitry Kamenetsky
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4 answers

Arrows on a Chessboard

I've taken an $n$ by $n$ chessboard and drawn an arrow on each square, pointing in one of the eight compass directions. I've done this in such a way that arrows in (orthogonally) adjacent squares differ by at most $45^\circ$. I place a cricket on…
Mike Earnest
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The largest integer made of 1,2,3,4

What is the largest integer $A$ that can be produced from the four digits $1,2,3,4$ subject to the following rules? Each of the digits $1,2,3,4$ is used exactly once. Juxtaposition of digits is allowed (so one may for instance juxtapose 1 and 3 to…
Gamow
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A flag-packing problem

An entry in Fortnightly Topic Challenge #45: Flags You are provided with a 9x9 grid of squares and 21 minimalistic flags (pictured below, all shown to scale). TASK: Assign a colour (Black, Blue, Green, Orange, Red, White, or Yellow) to each of…
Stiv
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28
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1 answer

A Company of Thirteen

These thirteen English words share a hidden property: cold, laughter, unblock, word, kill, witch, even, now, warm, oil, talking, potted, corn The list is not complete, there are other words with the same property, most don't fit the pattern though.…
Moghwyn
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28
votes
1 answer

Yes, this is the legendary wall

An entry in Fortnightly Topic Challenge #42: Wordless Connecting Walls This is it. This is the very wall. His life, his work — this wall was the center of it all. One simply cannot imagine his fame, greatness, and legacy without thinking about how…
Ankoganit
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28
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4 answers

1000 gold coins to share with the king

You are the knight of a great kingdom in an unknown world. Your king sent you to a dungeon and you killed the dragon and got 1000 gold coins from the dragon’s lair. Normally, you are supposed to give all gold coins to the kingdom but the King…
Oray
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Shifting a digit from right to left

A positive integer n (without leading zeros) has the property that shifting the rightmost digit of n to the left end doubles the number. Examples: 1->1, 1234->4123, 2020->202 What is the smallest n with this property?
ThomasL
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1 answer

Use three 10's to create 950

Here is an interesting puzzle that I found: You have three 10's. It looks like this: | 0 | 0 | 0 Add one stroke to the diagram to create 950.
WarpPrime
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4 answers

Short but impossible math problem

Given these four equations/inequalities: 1x=2 2x=4 3x=3 4x>8 What is x?
Ed Marty
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Hey, This is a 100th Puzzle of Mine!

Yep, this is my 100th puzzle here in PSE~ I'm really having a wonderful time here, thank you so much guys! >< I planned to write a harder and bigger one, but it turned out I was too lazy to do that.. So anyway, this is Minesweeper (Mine…
athin
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27
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4 answers

A COVID-19 puzzle: How large a class do you need to fit 30 pupils?

Some countries are proposing to reopen high schools soon. To ensure safety, they want to make sure that all pupils in a class are at least 2 m apart. To help them find the smallest room that can fit the pupils from one class, we need to solve the…
Simd
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5 answers

Google cannot find me

Google cannot find me, reflected I'm lemon and lime, googling 'me' is when you fall, me and meme will answer all. What am I? Line 1 hint: Posted I still have no matches in Google. Line 2 hint: Take my reflection as vertical, a…
Tom
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2 answers

The disappearance of Beastly Gerbil

Part 2: The entrapment of Beastly Gerbil Part 3: The escape of Beastly Gerbil This is an unusual call in. As a private detective you have been asked to investigate several odd cases, but this you're still convinced this one is taking the mick. You…
Beastly Gerbil
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Using burning ropes as timer - how to measure 1 hour and 8 minutes with 3 ropes?

This is a variation of a well known puzzle, you can find the other versions on PSE. You have three ropes and a box with ten matches. As usual each rope takes one hour to burn completely when lighted from any end but it does not burn uniformly. This…
melfnt
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