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 6 The Female Star My first two letters are a man. The first three a woman. The first four are a brave man. And in whole I am a brave woman. Submitted by Valentin Doable 4.3 8 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 ... Submitted by Valentin Hard 8.5 5 Betsy and Patsy “We were born on the same day of the same year,” said Betsy. “And we have the same mother and father,” said Patsy. “But we’re not twins!” the two exclaimed. Can you explain? Submitted by Valentin Doable 3.5 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 ... Submitted by Aakash Hard 7.7 16 100 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 ... Submitted by Aakash Hard 7.6 56 All the King's Wine So there's this king. Someone breaks into his wine cellar where he stores 1000 bottles of wine. This person proceeds to poison one of the 1000 bottles, but gets away too quickly for the king's guard ... Submitted by Aakash Hard 7.5 19 Going to the Track The London racetrack needs to submit its top three horses to the Kentucky Derby next month in order to compete for a prize. However in a recent electrical storm, all the racetrack's previous race histo ... Submitted by Nikhil Doable 6.2 18 Cocktail Party You are observing a cocktail party that has seven guests. You notice that each guest shakes hands with one another once they meet, but never again. How many handshakes occurred during the cocktail part ... Submitted by Nikhil Easy 2.4 12 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 ... Submitted by Raymond Doable 5.5 9 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? Submitted by city_slick Doable 5.0 10 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 ... Submitted by city_slick Easy 3.0 16 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 ... Submitted by Guilherme Hard 8.1 3 Products Algorithm Given an array A[1...N] of integers, create an array O[1...N] where O[i] = the product of all elements in A except for the ith element. For example, if N = 3, and A = {6, 4, 2}, O = {8, 12, 24} The t ... Submitted by ace25 Doable 4.0 13 Bit Pair Swap In one line of C or Java, how would you swap every pair of bits in a byte? That is, swap bits 0 and 1, 2 and 3, 4 and 5, 6 and 7. Example: 0110 1010 becomes 1001 0101. Submitted by Ravi Doable 6.6 45 The Sinking Island You and 3 friends are on an island that is sinking. There is one bridge from the island to the mainland that supports at most 2 people at once. However, it's dark outside so anyone crossing the bridge ... Submitted by Ravi Doable 4.3