Concept : numbers of consecutive natural numbers sum to n = (number of odd factors of n ) -1 1000 = 5^3 * 2^3here number of odd factors = 4 and required answer = 4 - 1 = 3

The clock loses 30 minutes per hour. i.e 30 minutes of this faulty clock = 60 minutes of the correct clock From 2 p.m to 6 p.m , total number of hours = 4 hours 4 hours of this faulty clock => 4 x 60/30= 8 hours of original clock So, The correct time when the clock show 6 p.m = 6 p.m + 4 = 10 p.m But The clock stopped 3 hours ago , So present time is 10 p.m + 3 hours = 1 a.m

Q100) A and B play a game of dice between them. The dice consist of colors on their faces (instead of numbers). When the dice are thrown, A wins if both show the same color; otherwise B wins. One dice has 4 red face and 2 blue faces. How many red and blue faces should the other dice have for both the to players have same chances of winning? a) 3 red and 3 blue faces b) 2 red and remaining blue c) 6 red and 0 blue d) 4 red and remaining blue

@venkateshp 6! Ways ................

@venkateshp Solution:To understand the answer,we need to reduce this problem to only 2 pirates. So what happens if there are only 2 pirates. Pirate 2 can easily propose that he gets all the 100 gold coins. Since he constitutes 50% of the pirates, the proposal has to be accepted leaving Pirate 1 with nothing. Now let’s look at 3 pirates situation, Pirate 3 knows that if his proposal does not get accepted, then pirate 2 will get all the gold and pirate 1 will get nothing. So he decides to bribe pirate 1 with one gold coin. Pirate 1 knows that one gold coin is better than nothing so he has to back pirate 3. Pirate 3 proposes {pirate 1, pirate 2, pirate 3} {1, 0, 99}. Since pirate 1 and 3 will vote for it, it will be accepted. If there are 4 pirates, pirate 4 needs to get one more pirate to vote for his proposal. Pirate 4 realizes that if he dies, pirate 2 will get nothing (according to the proposal with 3 pirates) so he can easily bribe pirate 2 with one gold coin to get his vote. So the distribution will be {0, 1, 0, 99}. Smart right? Now can you figure out the distribution with 5 pirates? Let’s see. Pirate 5 needs 2 votes and he knows that if he dies, pirate 1 and 3 will get nothing. He can easily bribe pirates 1 and 3 with one gold coin each to get their vote. In the end, he proposes {1, 0, 1, 0, 98}. This proposal will get accepted and provide the maximum amount of gold to pirate 5.(adsbygoogle = window.adsbygoogle || []).push({}); copied