How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Distances from you to certain cities are written below.

BERLIN 200 miles

PARIS 300 miles

ROME 400 milesAMSTERDAM 300 miles

CARDIFF ??? miles

How far should it be to Cardiff ?

In The 1st month of this year(the year 2013), I noticed that the date 13-1-13 (13 January 2013) is special.

This date is special as:

Date * Month = Year.

Can you figure out which year of this century has a maximum number of such dates?

Can you convert the number zero(0) into a positive number using just one mathematical operator ?

What is the centre of gravity?

Detective John was investigating a murder in China.
It was a difficult case, and John was completely stumped until he noticed a message sent to him by the killer cunningly hidden in a newspaper advertisement selling Car Licence Plates.
Detective John thought about it for a while, and when he had solved the puzzle, immediately arrested the guilty man.

Q1) How did John know the advert was a clue for him?

Q2) Solve the code and tell me who John arrested.

This is the newspaper advert (Car licence plates for sale) that Detective John saw.

Plates For Sale;

[W 05 NWO]
[H 13 HSR]
[O 05 EBM]
[D 08 UNE]
[U 10 HTY]
[N 04 BRE]
[N 16 TTE]
[I 26 LHC]
[T 10 AEE]
[I 26 CNA]
[X 22 VDA]

Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him "Why on Earth have you missed so many days?" Thomas replies "There just isn't enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that's 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days. Add all of that up and you get about 361 days. That only leaves 4 days for school." The principal knows Thomas is full of it, but can't figure out why. Where is Thomas going wrong?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

Replace the (?) with the correct mathematical signs to make the expression equal to 59.

18 ? 12 ? 4 ? 5 = 59

Until it is measured, not known. Yet how you miss it when it has gone. What is it?