In a guessing game, five friends had to guess the exact numbers of apples in a covered basket.
Friends guessed 22, 24, 29, 33, and 38, but none of the guesses was correct. The guesses were off by 1, 8, 6, 3, and 8 (in random order).

Can you determine the number of apples in a basket from this information?

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

How many letters are in the alphabet?

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?

What is wrong in the below Picture?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

I ask Joseph to pick any 5 cards out of a deck with no Jokers.

He can inspect then shuffle the deck before picking any five cards. He picks out 5 cards then hands them to me (Jack can't see any of this). I look at the cards and I pick 1 card out and give it back to Joseph. I then arrange the other four cards in a special way, and give those 4 cards all face down, and in a neat pile, to Jack.

Jack looks at the 4 cards i gave him, and says out loud which card Joseph is holding (suit and number). How?

The solution uses pure logic, not sleight of hand. All Jack needs to know is the order of the cards and what is on their face, nothing more.

A king sentenced a man to the death sentence for some crime he had committed. Known for his kindness, the king told the culprit that he had a choice to die in a way he decides.

The culprit was clever and said something that saved him from death. What method do you think he must have chosen for his death?

A man and his wife were doing missionary work near the city of Nairobi in the country of Kenya in eastern Africa. Their housing had not yet been completed, so the man, the woman, and their six year old daughter were spending a few nights in the jungle in three small pup tents. During their third night there, the woman was awakened by the call of a hyena passing by, so she got out of her tent to see if her young daughter had been frightened by the noise. As she peered into her daughter's tent she was surprised to see the dark figures of lion, a panther, and a cheetah which were curled up next to her daughter. Seeing her daughter was asleep and unharmed, the woman slowly and quietly withdrew from the tent, and simply returned to her own tent and went back to bed. How could this child's mother leave her daughter in such a dangerous situation, and simply ignore what she had just witnessed without intervening in some way? How can such emotional coldness ever be explained; or is there something here we are missing?

What is the largest number you can write with just 3 digits?