Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

Why is the Hole below a Lock?

There are three houses in a straight row. One is red, one is blue, and one is white. The red house is left of the middle. The blue house is right of the middle. Where's the white house?

Can you identify the direction in which this bus is moving; left or right?

Hint: The bus is moving on the roads of London.

A finger goes in me. You fiddle with me when you're bored. The best man always has me first. What am I?

What is the fewest number of coins that would be required in order to make sure each and every coin touches exactly three other coins?

I am the largest in my family of fifty.
The youngest of our family lives separately from the rest of the family and so do I.
I am regarded as harsh and tough.
I am so large, you cut me in two equal halves,
each half would still be larger than the second largest member of the family.
Who am I?

In particular commonwealth games, a female participant won silver and gold medals for a single event.

How can this be possible?