Solution:

Form an equilateral triangle. Now place three cones on the vertices. Now place one cone on each of the three edges, at their middle point. The last cone must be kept at the centroid of the triangle.

In this manner, you will get 3 rows corner to corner and 3 rows via the centroid and each will have 3 cones only.

Solution:

The person on 73rd number will survive.

Explanation:
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.

Solution:

60 minutes

Explanation:
Roy will be able to consume all the five tablets in an hour.

Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.

Solution:

3/7

Explanation:
If a 31day month starts on a Friday, Saturday or Sunday it will have five Sunday, if not it will have 4 Sunday.

Solution:

Michelangelo juggles the diamonds across while crossing the bridge.

Solution:

8/(1−1/5)

Solution:

What must be kept in mind before you start calculating through any method is that the weights can be put on both the pans.

So the weights - 1, 3, 7, 12, 43, 76, 102

The oldest man that can be weighed using these weights is a man aged 122 years

Solution:

Blue could only be wearing white or red and we know that there is already someone else wearing the white shirt so Mr. Blue could only be wearing the red shirt.

Mr. White could have only been wearing a blue or a red shirt, and red is already taken, so Mr. White is wearing a blue shirt.

Mr. Red now has to be wearing a white shirt.

Solution:

The man asked the king that he wanted to die of old age.

Solution:

888 + 88 + 8 + 8 + 8 = 1000

Solution:

I filled a glass full of water and held it over my head for 20 minutes.