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?

Can you solve below mathematical equation?

2^1234 - 2^1233

I can be cracked, made, told, and played. What am I?

Dwayne Johnson was running away with the loot from a heist in his car along with Vin Diesel. One tire was punctured and he dropped down to replace it. While changing the wheel, he dropped the four nuts that were holding the wheel and they fell into a drain. Vin Diesel gave him an idea using which they were able to drive till the rendezvous point.

What was the idea ?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

What does this rebus riddle means ?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

In a rainy season, one day 3 huge ladies walked under a normal-sized umbrella.
The umbrella is not huge enough to accommodate all 3 ladies yet not a single lady got wet. Why?