A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

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

If all the below statements are true

1. Gianni was either in Italy or France in 1997.
2. If Gianni did not kill Versace, Hilton must have killed him.
3. If Versace died of suffocation, then either Gianni killed him or Versace committed suicide.
4. If Gianni was in Italy in 1997, then Gianni did not kill Versace.
5. Versace died of suffocation, but he did not kill himself.

Who killed Versace and where was Gianni in 1997?

In the image given, you can find several triangles. Can you count them all?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

I organized a small get together at my home.
In the party , i have a barrel with some whiskey in it.

Suddenly Guest 1 say 'I bet this barrel of whiskey is more than half full'.
'No, it's less than half full' Guest 2 replied.

I don't have any measuring instrument and without removing whiskey from it , how can i determine which of the guest is right ?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

If 21x = 79x, what is the value of x?