How do you go from 98 to 720 using just one letter?

The square root of number 121 is "11". What is the square root of the number "12345678987654321."?

Why is the Hole below a Lock?

What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

How can you drop a raw egg from a height onto a concrete floor without cracking it?

Three men in a cafe order a meal the total cost of which is $15. They each contribute $5. The waiter takes the money to the chef who recognises the three as friends and asks the waiter to return $5 to the men.

The waiter is not only poor at mathematics but dishonest and instead of going to the trouble of splitting the $5 between the three he simply gives them $1 each and pockets the remaining $2 for himself.

Now, each of the men effectively paid $4, the total paid is therefore $12. Add the $2 in the waiters pocket and this comes to $14. Where has the other $1 gone from the original $15?

Can you find out the total number of triangles in the given figure?

Two in a corner, one in a room, zero in a house, but one in a shelter. What am I?