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6
4
Sum of Two Prime Numbers
If p, q > 2 are consecutive in set of primes. Since p,q can only be odd number, (p+q) is an even number.
Can (p+q)/2 be prime?
from http://republicofmath.com/
Submitted by MoralMachine
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Easy
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4
Matchsticks
This is a classic Martin Gardner puzzle.
See the picture - the four matchsticks represent a martini glass and the match head represents an olive. Move just two matches so that the glass is reformed bu
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Doable
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9
11
3 Coins
Not sure what the answer is, ideas welcome!
You have 3 coins, one always comes up heads, the second always comes up tails, and the third is a fair coin. You select a coin at random. After selecting
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Easy
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8
5
The double-square number problem
It's said that a number N with 4 digits is a double-square number when it equals the sum of the squares of two numbers: one formed by the first two digits of N, in the order they appear in N and the ot
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Hard
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9
4
Carpeting a Donut
Given two concentric circles and a chord of the outer circle, tangent to the inner circle, of length 25m, find the area between the two circles. See illustration. No other information needed, all you n
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Doable
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8
4
The Monty Hall Problem
You’re on a game show, and you’re given the choice of three doors: Behind one door is a car and behind the other two doors are goats.
You pick a door, say No. 1, and the host, who knows what’s behind
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Doable
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3
Grey Squares Illusion
Square A is the exact same shade of gray as square B.
It's true, check out the reconstruction.
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Doable
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3
Count The Bits
Write a function that counts the number of bits in an integer that are set to 1 that is linear in time complexity in the worst case, but sub-linear on average.
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Doable
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11
100 Light Bulbs
There are 100 light switches, all of them are off. First, you walk by them, turning all of them on. Next, you walk by them turning every other one off. Then, you walk by them changing every third on
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Hard
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7
Two Trains
Two trains (Train A and B) with 200 km between them are travelling towards each other at 100km/h. A mosquito, initially standing on the front of Train A, starts travelling towards Train B at 150km/h. O
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Doable
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9
7
Coin Flip
On Monday, you flip a coin all day. You start flipping it until you see the pattern Head, Tail, Head. You record the number of flips required to reach this pattern, and start flipping again (and co
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Doable
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9
2
Fork in the road
You are walking down a road and arrive at a fork that splits the road into two separate paths. When you reach, you meet two identical twins, each standing at the edge of one of the two paths. You h
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Submitted by Aakash
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Doable
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6
2
Prisoners and hats
100 prisoners are standing in a line each 1 seeing the back of the ones in front of him. Each prisoner is given a black or a white hat. If they can guess the color of their hat they can go away freel
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Hard
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7
Unfair Coin
Say you have an unfair coin: a coin whose probability of flipping heads and flipping tails is unknown but nonzero.
Can you design a game where you and your opponent have an equal chance of winning?
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Doable
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3
5
Balloon in an Elevator
A person is holding on to a helium balloon in an elevator. The elevator cable snaps, and at the exact same moment, the person lets go of the helium balloon. In the perspective of the person in the el
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Hard
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