How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

Spot 5 differences in two Christmas tree below:

John is found dead in a bare field. Nobody killed John,
John did not commit suicide.

Inspector Jacob found a bag just a few meters away from John which could save his life. What was in the bag?

A cricket has 6 legs, a squirrel has 4 legs and a spider has 8 legs.

In a local zoo, it was found that the total number of legs is 612. Also, there are equal number of each of the above animals/insects.

Can you find out how many animals are there in the zoo?

Two guards were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?"

How did he know his companion was smiling?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

There is something which you can be arrested for attempting but not for successfully completing.

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

One is to three as three is to five and five is to four and four is the magic number.
What is the pattern?

I cannot talk, but I always reply when spoken to. What am I?