What begins with T, ends with T, and has T in it?

What does this mathematical rebus means ?

There are four 3-link chains. All you have to do is join them into a big 12-link chain. For joining two closed links, one of the links must be cut and placed onto the other link for closing.

How many minimum links will you have to cut to make the big chain?

There are are five things wrong with this sentence; only geniuses will be able to to spot all of the mitstakes

Sally lives in a place where six months of the year is mild summer and the temperature drops significantly the other six months. She owns a lake where there is a small island. She wants to build a house on the island and needs to get materials there. She doesn’t have a boat, plane, or anything to transport them to the island. How does Sally solve this problem?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

My first is in chocolate but not in ham. My second is in cake and also in jam. My third at tea time is easily found. Altogether, this is a friend who is often around. What is it?

When monkey rotate the gear, which mark will be hit 1 or 2 ?

How can a man go eight days without sleep?

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.