Find the number of unordered triplets of boolean operations (AND, OR, XOR, XNOR, NOR, NAND, IMP, and IMPBY) that are sufficient to uniquely determine the values of two ordered bits.
Let us say there are two natural numbers "L" and "R". We performed eight operations on these two numbers as
Step-1: L = R Step-2: L x L = R x L Step-3: L^2 - R^2 = LR - R^2 Step-4: (L + R)( L - R) = R(L - R) Step-5: L + R = R Step-6: R + R = R Step-7: 2R = R Step- 8: 2 = 1
What is wrong here?
Calculate the number of ordered triples (A1, A2, A3) such that:
A1 ∪ A2 ∪ A3 = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A1 ∩ A2 ∩ A3 = ∅
Write your answer as 2a3b5c7d where a, b, c, d are non-negative integers.
You've got 27 coins, each of them is 10g, except for 1. The 1 different coin is 9g or 11g (heavier, or lighter by 1g). You should use balance scale that compares what's in the two pans. You can get the answer by just comparing groups of coins. What is the minimum number weighings that can always guarantee to determine the different coin.
