Can you name four days which start with the letter 'T'?

A crime was committed at baker street. Ibrahim Dakota who was shot in the stomach was the main suspect. Sherlock questioned the suspect. The conversation started as:
Sherlock: What's your story, Ibrahim?
Ibrahim: I was walking around baker street and suddenly a man from the back shot me. I ran as fast as I could to save my life".
Sherlock: That is enough (and ask the police to arrest him).

Why does Sherlock think he is the murderer?

I am quite hot but become too cold if you remove the first two letters. What am I?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?

By including only four matchsticks in below picture, you have to make "Four Triangles And Two Squares"

In a supermarket, there is an intelligent glass pane before a refrigerating unit. This glass pane allows cherries and apples through it but does not allow grapes and Orange to pass through it.

Can you identify the rule that the glass pane is following?

There are hundred red gems and hundred blue gems. The blue gems are priceless while the red gems equal wastage. You have two sacks one labeled Heads and the other Tails. You have to distribute the gems as you want in the two sacks. Then a coin will be flipped and you will be asked to pick up a gem randomly from the corresponding sacks.

How will you distribute the gems between the sacks so that the odds of picking a Blue gem are maximum?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

Double it and multiply it by 4. Then divide it by 8 and you’ll have it once more. What number is it?