Can you solve this amazing hard number series problem?
7, 8, 10, 12, 16, 18 ?

Find the next number in the series below.

6 18 270 72090 ?

You have two rectangular wires.

Both of them have property that when you light the fire from one end , it will take 60 minutes to get completely burn.

However, they do not burn at consistent speed (i.e it might be possible 1st 20% burn in 50 minutes and 80% can burn in 10 minutes).

So how could you measure 45 minutes ?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

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?

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

A gardener planted the Lemon trees in a mathematical ordered way (i.e. he planted a tree in rows).
He created a total of 19 rows of trees.

Note: There should be more than 2 trees to count as a row.

What is the minimum number of trees required by the gardener to have 19 rows of trees?

You are on your way to visit your Friend, who lives at the end of the hill. It is his birthday, and you want to give him the cakes you have made. Between your house and his house, you have to cross 5 bridges, and as it goes in the land of make believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake. How many cakes do you have to leave home to make sure that you arrive at a friend's house with exactly two

In the city of Brain Teasers, 5% of people do not list their phone numbers. Now if we select random 100 people from the phone directory, then how many people selected will have unlisted phone numbers?

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?