Find out a multi-digit number that if multiplied by the number 9 or any of its multiplications products (i.e. 18, 27, 36, 45,..) will result in the multiplication factor repeated (n) number of times.

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

Can you decipher the two rows to find the hidden word?

using four eights (8) and a one (1) and one mathematical symbol , create the number 100

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

John was going on a jungle trip. He asked his wife to pack something to eat, something to drink and something to burn if he feels cold in the jungle. When John opens the backpack he found just one thing in the bag. What was it?

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.)

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?

I have a hole in my back and legs I lack.
I live where I can’t breathe and I eat without teeth.
What am I?