What's the only room from which no one can enter or leave

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

By adding four matchsticks, can you divide the square shown in the picture into two equal parts?

It has a long neck, A name of a bird, Feeds on cargo of ships, It's not alive,

What is it?

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

The Puzzle: A girl, a boy, and a dog start walking down a road.

They start at the same time, from the same point, in the same direction.

The boy walks at 5 km/h, the girl at 6 km/h.

The dog runs from boy to girl and back again with a constant speed of 10 km/h. The dog does not slow down on the turn.
How far does the dog travel in 1 hour?

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

What has no start, end, or centre?

Can you divide numbers from 1 to 9 (1 2 3 4 5 6 7 8 9) into two groups so that the sum of the numbers of each group is equal?

Note: 9 cannot be turned over to make it 6.

Can you convert the number zero(0) into a positive number using just one mathematical operator ?