An intelligent trader travels from one place to another with 3 sacks having 30 coconuts each. No sack can hold more than 30 coconuts. On the way, he passes 30 check points. At each check point, he has to give one coconut for every sack he is carrying. What is the maximum number of coconuts that he can have with him at the end of his journey?
He will have 25 coconuts with him at the end. The trick is to reduce the number of sacks as you pass checkpoints. The first 10 checkpoints require 3 coconuts each, which empties his first sack. The next 15 checkpoints require 2 coconuts each, which will empty his second stack. Now, he is left with 1 sack and 5 more checkpoints. So, the 5 checkpoints will take 1 coconut each. Therefore, he will be left with 25 coconuts.
A man puts on a clean shirt every night before bed. On the first nigh he puts on a blue shirt. He than sleeps for 5 hours. Every one hour more he sleeps than the night before he put on a different color shirt the next night according to this scale: blue, black, red, green, white, pink, orange, brown, purple, yellow, grey, neon green, tan, and teal. Every one hour less he sleeps than the last night he put on a different color shirt the next night going backwards on his scale.
If he were to wear a blue shirt because he slept more hours than the last night he does. If it was because he slept less hours than the night before he skips it and wears a teal shirt instead. If he goes backwards on the scale and goes to blue but would not wear a blue shirt he still counts blue in his going backwards on his scale.
The second night the man wears a blue shirt because he did not sleep any more or less hours than the last night. The man sleeps for six hours that night.
The next night he sleeps for five hours.
Night number four he sleeps for eight hours.
The next night he sleeps for seven hours.
The next night he sleeps so well he sleeps for 11 hours.
Night number seven he stays up so late he only sleeps for four hours.
The next night he is so tired he sleeps for eight hours.
The next night he sleeps for eight hours again.
Night number ten he sleeps for 14 hours because he is sick.
Since he slept so long the last night he only sleeps for seven hours.
The next night he is a little bit tired so he sleeps for eight hours.
The night after that he had to do so much work he only slept five hours.
The next night at work they let him out early and he slept for nine hours.
The next night he slept for eight hours.
And the last night the man did he slept for ten hours.
The next night he put on a different color shirt according to his scale, but the next night he randomly picked a shirt. At what night will the man wear a blue shirt again?
100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left. Which number survives at the last?
73rd person will survive at last.
If the number of players is the power of 2, the last person to survive will be the one who started it.
But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number of players (100) which is 64.
So when starting with 100 players - we need to kill 36 of them to get down to a power of 2 (64). Since we kill every other person starting at player 2 the last person we need to die is player 72, they will be killed by player 71 and the first person in the effective power of 2 game, who will win is player 73.
It's worth noting that this process of reducing to a power of 2 will always be completed in the first round regardless of the number of players.
Consider X players, let Y be the highest power of 2 that is less than or equal to Y
The winning player is 2 * (X - Y) + 1
