Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

You have two buckets of 11 liters and 6 litres.
How can you measure exactly 8 litres?

John speaks the truth only once a day in a week. Below are a few hints for you:

First: Days are Sunday, Monday and so on.
Second: One day he says, "I lie on Monday and Tuesday".
Third: On the next day, he says, "Today is either Thursday, Saturday or Sunday".
Fourth: On the next day, he says, "I lie on Wednesday and Friday".

Can you identify the day on which he speaks the truth?

The husband and wife were jogging in the morning. To match every two steps of the husband, the wife required three steps. If Both of them start with the here right foot. After how many steps do their left foot be together?

A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?

A river should be crossed by a father, a mother and their two sons and two daughters.
There are some rules that should be followed while crossing the river. There can be only two people in the raft while crossing. The daughters cannot be with their father unless there is the presence of the mother. The sons cannot be with their mothers unless the father is present. Unless the guard is on the board, the criminals cannot be with any of the family members. Only the adults like the father, the guard, and the mother knows to use the raft.

How will they cross the river?

The below given figure comprises of a pattern through which you can determine the missing letter. Can you push your mind to find the pattern and add the missing letter?

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?