A king has 100 identical servants, each with a different rank between 1 and 100. At the end of each day, each servant comes into the king's quarters, one-by-one, in a random order, and announces his rank to let the king know that he is done working for the day. For example, servant 14 comes in and says "Servant 14, reporting in."
One day, the king's aide comes in and tells the king that one of the servants is missing, though he isn't sure which one.
Before the other servants begin reporting in for the night, the king asks for a piece of paper to write on to help him figure out which servant is missing. Unfortunately, all that's available is a very small piece that can only hold one number at a time. The king is free to erase what he writes and write something new as many times as he likes, but he can only have one number written down at a time.
The king's memory is bad and he won't be able to remember all the exact numbers as the servants report in, so he must use the paper to help him.
How can he use the paper such that once the final servant has reported in, he'll know exactly which servant is missing?
When the first servant comes in, the king should write down his number. For each other servant that reports in, the king should add that servant's number to the current number written on the paper, and then write this new number on the paper.
Once the final servant has reported in, the number on the paper should equal
(1 + 2 + 3 + ... + 99 + 100) - MissingServantsNumber
Since (1 + 2 + 3 + ... + 99 + 100) = 5050, we can rephrase this to say that the number on the paper should equal
5050 - MissingServantsNumber
So to figure out the missing servant's number, the king simply needs to subtract the number written on his paper from 5050:
MissingServantsNumber = 5050 - NumberWrittenOnThePaper
See also best riddles or new riddles.logicshort
The day before yesterday Cindy was 17. Next year she will be 20. How can this be?
The statement was made on January 1. Cindy's birthday is on December 31. She was 17 the day before yesterday (Dec 30). She was 18 yesterday. She will be 19 this year (Dec 31) and 20 next year. logicshort
During the Summer Olympics, a fellow competed in the long jump and out-jumped everybody. He didn't just win the event, he actually broke the world record held for that event. Nobody broke his record for the remainder of the Olympics, and still today his name is in the record books.
However, even though he holds the world record, he never received a medal in the long jump. How did he manage to do so well, but not receive a medal?
He was competing in the decathlon. He won the long jump event, but didn't perform very well in the other events. He lost the decathlon, so he didn't receive any medals (even though he hold the world record for long jump). logicshort
How far can you run into the woods?
Half way. If you go in any further, you’d be running OUT of the woods.logicshort
Name the only sport in which the ball is always in possession of the team on defense, and the offensive team can score without touching the ball?
What country is hidden in the paragraph below?
As defendants, we deny all involvement in the unscrupulous dealings which have come to light in the recent government investigation.
I eat other animals.
I have a big mouth.
I am green.
I live in the water.
Who am I?
I am a crocodile. logicscaryshort
It was very dark. There was no electricity in the house. They had no candles or lanterns. The house was completely dark. A girl was reading and preparing for her exams. How?
Simple! The girl was blind and she was reading through Braille method. logicshort
There were two women, standing and facing the opposite ways. The first lady was facing south and the second lady was facing north. But, they could see each other. How is that possible?
They were holding the mirror. logicshortwhat am I
I am a five letter word. If you remove all letters one by one from the last, I sound the same! What am I?
QUEUE! QUEU! QUE! QU! Q!logicmathshort
Two planes take off at the same exact moment. They are flying across the Atlantic. One leaves New York and is flying to Paris at 500 miles per hour. The other leaves Paris and is flying to New York at only 450 miles per hour. Which one will be closer to Paris when they meet?
They will both the same distance from Paris when they meet!