Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

Name a key which is hardest to turn.

The world's largest Thanksgiving turkey was on display at a fair. Everyone was admiring it when suddenly a woman ran up and shot the turkey and left. Everyone knew her yet nobody made any attempts to stop or report her. Why?

John was working on a Chemical Mixture whose weight comprise 90% liquid and 10% solid. The total weight of the mixture is 20 pounds. After a while, John noticed that some of the liquid evaporated and now the liquid comprises just 50% of the weight.

What is the weight of the chemical mixture now?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

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?

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?

Which is the smallest number that you can write using all the vowels exactly once?

How can you make number one disappear by adding something to it?