With the help clues provided in the image, can you find the 5 digit key?

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

A farmer went to a market and bought a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer’s challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it?

When I get multiplied by any number, the sum of the figures in the product is always me. What am I?

My location can be determined by the below rebus.
So where am i ?

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

Railroad Crossing, look out for the cars. Can you spell that, without any R's ?

By moving exactly three matchsticks can you make the below equation true.It can be solved by 3 ways.

Why 1729 is a magic number? Answer Logically.

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