What number should come in place of the question mark below?

Find the next number in the sequence

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

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different.

How do you measure 45 minutes?

In a box, there is a jumble of 7 red balls, 6 blue balls, 5 green balls, and 4 yellow balls. What is the minimum number of balls, will you have to pick up so that you have at least 4 balls of the same colour?

You have two buckets - one holds exactly 5 gallons and the other 3 gallons. How can you measure 4 gallons of water into the 5 gallon bucket?

(Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.)

What Adam and Eve do not have but the rest of the people have?

In the addition below, all digits have been replaced by letters. Equal letters represent equal digits and different letters represent different digits.
ABCABA
BBDCAA
ABEABB
ABDBAA
------- +
AAFGBDH
What does the complete addition look like in digits?

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

You are given with the following sum. Each of the letters can be decoded as a digit. If we tell you that D = 5, then can you solve it entirely?

DONALD
+GERALD
=ROBERT

Your job is to measure 45 minutes if you have only two cords and matches to light the cords.

1. The two cords are twisted from various materials, so their different segments can burn at different rates.
2. Each cord burns from end to end in exactly one hour.

Describe your way of measuring the 45 minutes.