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 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 12 Choose the Next Letter Choose the next letter in the sequence: O T T F F S S ? Submitted by Ravi Doable 3.8 12 Simple 24 Why is that if p is a prime number bigger than 3, then p^2-1 is always divisible by 24 with no remainder? Submitted by Aakash Doable 6.6 12 Gold or silver? What weighs more, a pound of silver or a pound of gold? Submitted by Jango Easy 2.0 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 11 Measuring Up You have a 3 and a 5 litre water container, each container has no markings except for that which gives you its total volume. You also have a running tap. You must use the containers and the tap in su ... Submitted by Ravi Easy 3.1 10 Mutilated Chessboard Problem Suppose a standard 8×8 chessboard has two diagonally opposite corners removed, leaving 62 squares. Is it possible to place 31 dominoes of size 2×1 so as to cover all of these squares? Submitted by Ravi Hard 7.8 10 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 ... Submitted by Ravi Doable 4.5 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 10 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 ... Submitted by Aakash Doable 6.0 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 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 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 Three Idols Here's a classic: Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a comp ... Submitted by Aakash Hard 9.1 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