If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

Replace the question mark with the number below given a simple math problem.

Place a mathematical symbol between the numerals 5 and 9 in such a way that the resulting number is greater than 5 but smaller than 9.

What is the largest number you can write with just 3 digits?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?

Can you find a number that lies one third of the distance between 1/3 and 2/3?

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

I have thought of a number that is made up by using all the ten digits just once. Here are a few clues for you to guess my number:

First digits is divisible by 1.
First two digits are divisible by 2.
First three digits are divisible by 3.
First four digits are divisible by 4.
First five digits are divisible by 5.
First six digits are divisible by 6.
First seven digits are divisible by 7.
First eight digits are divisible by 8.
First nine digits are divisible by 9.
The number is divisible by 10.

Can you find out the number ?

You have 1023 apples and 10 bags. You have to distribute these apples in these 10 bags in any way you choose. But when I ask for a certain number of apples you have to give them in terms of bags without transferring the apples from other bags. How do you distribute the apples?

Your last good ping-pong ball fell into a narrow metal pipe embedded one foot deep in concrete.
How can you get it out undamaged, if all the tools you have are your tennis paddle, shoe laces, and plastic water bottle, which does not fit into the pipe?