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 21 Odd Pills Your pharmacist gives you 5 jars filled with pills. The pills contained in each jar have an identical appearance and size (i.e. if you mixed all of the pills you wouldn't be able to tell them apart). ... Submitted by Jay Elliott Doable 3.6 15 Swap Variables in Place without XOR Suppose you have two variables, a and b. How can you swap their values without using a temporary variable and also without using the bitwise operator XOR? Submitted by Valentin Doable 3.9 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 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 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 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 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 6 Binary 5 digits What is the base 10 equivalent of the highest 5 digit binary number? Submitted by Heather Moore Easy 2.0 18 3 Men and a Hotel Room Three men decided to split the cost of a hotel room. The hotel manager gave them a price of \$30. The men split the bill evenly, each paying \$10, and retired to their room. However, the manager real ... Submitted by Valentin Doable 4.2 8 Survivor There are 1500 people sitting around a circular table. They are numbered in a regular manner (1 to 1500 along the table). Now, the 1st person gets a sword and kills the 2nd person. He then gives the s ... Submitted by Shaheen Hard 8.5 7 Cooking Time A cook must put a souffle exactly 9 minutes at the oven, but he only have a 7 minutes hourglass and a 4 minutes hourglass. How can he measure 9 minutes with those clocks? Submitted by Ravi Doable 5.7 8 The Famous Hole in a Sphere This incredible problem was first made famous by Martin Gardner with his ‘Mathematical Games’ column published in Scientific American throughout the 60s and 70s. A cylindrical hole, 6 inches long, ... Submitted by Ravi Hard 6.7 10 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 Easy 3.2 9 1978 The year 1978 is such that the sum of the first two digits and the latter two digits is equal to the middle two digits, i.e. 19 + 78 = 97. What is the next year (after 1978) for which this is true? Submitted by Ryan Miller Doable 6.6 9 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 ... Submitted by Ravi Doable 5.5