A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

What is black when you buy it, red when you use it, and gray when you throw it away?

When a clock is observed, the hour hand is at a minute mark and the minutes hand is six minutes ahead of it.

When the clock is observed again after some time, the hour hand is precisely on a different minute mark and the minute hand is seven minutes ahead of it.

Can you calculate how much time has elapsed between the two observations?

Take one out and scratch my head, I am now black but once was red. What am I?

1 + 9 + 8 = ?
considering, 28 + 8 + 92 = 10

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

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 mathematics teacher took exams for his students. Out of the total students, 25% passed both the tests included in the exam. However, only 42% were able to clear the first test.

Can you find out the percentage of those students who passed the first test and also passed the second test?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?