What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

I know a 5-digit number having a property that With a 1 after it, it is three times as large as it would be with a one before it.

Guess the number?

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

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?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

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 ?

What four weights can be used to balance from 1 to 30 pounds?

If 2 workers can complete painting 2 walls in exactly 2 hours.

How many workers would be needed to paint 18 walls in 6 hours?