The centre of the third figure is empty. What digit should fit inside?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

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?

Can you count the number of triangles inside a triangle?

Find the next number in the series below

21 32 54 87 131 ?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

Three people enter a room and have a green or blue hat placed on their heads. They cannot see their own hat but can see the other hats.
The colour of each hat is purely random. They could all be green, blue, or any combination of green and blue.
They need to guess their own hat colour by writing it on a piece of paper, or they can write 'pass'.
They cannot communicate with each other in any way once the game starts. But they can have a strategy meeting before the game.
If at least one of them guesses correctly they win $10,000 each, but if anyone guesses incorrectly they all get nothing.
What is the best strategy?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from the above-mixed cards to guarantee at least one 'four of a kind?

What does this rebus means ?