Find the next number in the sequence

1, 2, 6, 21, 88, __?

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

Can anyone tell me a word in the English dictionary which has a silent 'z'?

Jim has three close friends at his school: Michael, John and Alice. Two of them play football, two play basketball and two play hockey. The friend who does not play hockey does not play basketball as well. The friend who does not play football does not play hockey.

Can you identify which sport/s is played by which person?

Alpha is Beta's sister.

Gamma is a Beta mother.

Delta is Gamma's father.

Tango is Delta's mother.

Then,

How is Alpha related to Delta?

There were two grandmothers and their two granddaughters.
There were two husbands and their two wives.
There were two fathers and their two daughters.
There were two mothers and their two sons.
There were two maidens and their two mothers.
There were two sisters and their two brothers.
Yet there are only six, who are buried here,
All are born legitimate and relationships clear.
How can this happen?

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

What have one eye but still cannot see?