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 ?

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!

John needs to purchase 100 chocolates from three different shops and he has exactly 100 rupees to do that which he must spend entirely. He must buy at least 1 Chocolate from each shop.

The first shop is selling each chocolate at 5 paise, the second is selling at 1 rupee and the third is selling at 5 rupees.

How many chocolates should he buy from each shop?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

Can you make the number 24 by utilizing the numbers 1, 3, 4 and 6? You must use one number only one time and you can use mathematical operation symbols anytime anywhere.

How do you go from 98 to 720 using just one letter?

A network of 20 x 10 squares is given to you.

Can you calculate how many unique squares and rectangles can be formed combining two or more individual squares ?

Use the digits from 1 up to 9 and make 100.

Follow the rules.
=> Each digit should be used only once.
=> You can only use addition.
=> For making a number, two single digits can be combined (for example, 4 and 2 can be combined to form 42 or 24)
=> A fraction can also be made by combining the two single digits (for example, 4 and 2 can be combined to form 4/2 or 2/4)

Question: how can we do this?

You need to arrange three 7 and mathematical symbols to form number 1?

Using Only Five 5's and any mathematical operator make sum as 37