3 Coins
SPOILER DON'T READ THIS BEFORE TRYING TO SOLVE THE PUZZLE SPOILER ************** * * * * * * * * * * My answer: First case. Since you are going to get heads twice it necessarily means you did not choose the Tails coin. This gives you two scenarios: 1  1/2 chance of choosing the fair coin times 1/2 chance of getting heads again. 2  1/2 chance of choosing the Heads coin times 1 chance of getting heads again, (1/2 * 1/2) + (1/2 * 1) = 3/4 or 75% For the second case. Three scenarios: 1  1/3 chance of choosing the Heads coin times 1 chance of getting Heads twice. 2  1/3 chance of choosing the Tails coin times 1 chance of getting Tails twice. 3  1/3 chance of choosing the fair coin, but since you've already got the same result twice, you only have the probability of getting the same outcome twice again which would be 1/2 * 1/2 = 1/4. 1/3 * (1 + 1 + 1/4) = 3/4 or 75% Did this pretty quick, not sure if I'm right. context 
Cocktail Party
Simple combination: 7! / ( 2! * (72)! ) context 
Nice to meet you
**** SPOILER ALERT Combination of N people in pairs: N! / (2! * (N2)!) = 45 N * (N  1) = 90 N = 0 or N = 10 which is the answer. context 
15
8
The doublesquare number problem
It's said that a number N with 4 digits is a doublesquare 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
