A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

While house hunting in London, I came across a very good leasehold property Discussing the lease the landlady told me:

'The property was originally on a 99 years lease and two-thirds of the time passed is equal to four-fifths of the time to come. Now work it out for yourself and see how many years are to go!

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

Can you find the missing letter in the sequence?
S - T - I - L - ? - T - F - Y - C

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

In a fruit store, there was a unique weighing machine that was made to weigh only cherries and strawberries as they were priced the same.

Other fruits like watermelons or mango had different machines as they were expensive.

A man successfully buys watermelons at the price of cherries. How?

What do you see in the given picture?

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.