What does an Island and the letter T have in common?

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?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

John's five friends Rachel, Jacob, Phoebe, Joey and Chandler live on the same road.

Rachel lives in the house: A, Jacob lives in the house: B, Phoebe lives in the house: C, Joey lives in the house:D, Chandler lives in the house: E

Mathematically
B*C*D = 1260
B + C + D = 2E
2A = E

The road numbers run from 2 to 222.

Can you tell me the house number of each of John's friends?

Solve the alphametic puzzle by replacing the alphabet with the number.

S T O R M +
S O L E S
=========
T O W E L
=========

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

Which letter of the alphabet has the most water?

Can you find the ages of a son, father and grandfather based on the following facts?
The sum of the ages of grandfather, father and son is 140 years.
The age of the son in months is the same as the grandfather in years.
The age of the son in days is the same as the father in weeks.