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 17 Multiples of 8 plus 1 Squaring the first several odd numbers reveals the following pattern: 3 squared = 8 + 1 5 squared = 24 + 1 7 squared = 48 + 1 8, 24, and 48 are all multiples of 8. Does this pattern hold for all squa ... Submitted by Heather Moore Doable 4.5 6 Grey Squares Illusion Square A is the exact same shade of gray as square B. It's true, check out the reconstruction. Submitted by Ravi Doable 6.0 8 Non-Adaptive 12 Identical Balls Okay - so I posted this puzzle to reddit a few weeks ago and one guy had the following comment: Same problem, but your solution must be non-adaptive. IOW, specify the weighings that you will make up f ... Submitted by Aakash Hard 9.0 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 11 Gold or silver? What weighs more, a pound of silver or a pound of gold? Submitted by Jango Easy 2.0 37 No if() Only abs() Given two variable a and b, construct a function f(a,b) which return the maximum one in {a,b}. You can only use +- · / and abs() (to take the absolute value). NO if() is allowed in your construction. ... Submitted by MoralMachine Doable 5.8 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 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 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 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 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 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 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 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