A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

Find the next number in the series below

21 32 54 87 131 ?

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 ?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

If,

A + B = C
D - C = A
E - B = C

Based on the above equations, find out the answer for:

D + F = ?

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?

Sally lives in a place where six months of the year is mild summer and the temperature drops significantly the other six months. She owns a lake where there is a small island. She wants to build a house on the island and needs to get materials there. She doesn’t have a boat, plane, or anything to transport them to the island. How does Sally solve this problem?

A pregnant woman is preparing to name her seventh child. Her children's names so far are Dominique, Regis, Michelle, Fawn, Sophie, and Lara. What will she name her next child -- Jessica, Katie, Abby or Tilly?

This is a game of Tic-Tac-Toe which you all might have played innumerable times. Here, we are playing with the black and white markers instead. Also, there is a bit change to the rules. The changed rules allow you to play just three times. After the three markers are put by each of the players, you can only slide your marker into an empty square that shares a common wall with the square that the marker is leaving. You can refer to the figure given. If this is the position of the game, the white's next move would be from 6 to 3. Now, whatever the black one does, the white one will move his marker from 5 to 2 and he will have a three in a row. What you have to decide is if both of the players are using a perfect strategy, will the white player (who plays first) always win? Or it will be the black one who will win always? Or every game will be a draw?

You see a boat filled with people, yet there isn’t a single person on board. How is that possible?