What number when divided in half becomes zero?

I have an apple tree , number of apple in this tree get doubles every week.

On 30th week , the tree gets completely filled with apples :-)



Can you tell me , on what week does my tree is half covered with apples ?

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

If I put in one canary per cage, I have one bird too many. If I put in two canaries per cage, I have one cage too many. How many cages and canaries do I have?

You are mixing a mixture of cement and Sand with five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four-gallon bucket and a seven-gallon bucket and neither has graduation marks. Find a method to measure five gallons.

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

How can one talk without saying a single word?

A deaf and mute man goes to the train station. Tickets for the train are 50 cents each. The man goes to the ticket booth and hands the man inside just a dollar. The man in the booth hands him two tickets.

How did the man in the booth know to give him two tickets without even looking at him?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

I am white when I am dirty, and black when I am clean. What am I?