Can you find the number?

82. The Counterfeit coins

During my last visit to the U.K. I spent a few days in a small town, where I stayed as a playing guest with a British landlady. The heaters in the rooming house were all coin operated.

One day my landlady requested my help in sorting out a problem.

There were one hundred and twenty coins in her gasmeter and one of them, she knew, was counterfeit. The counterfeit coin was either heavier or lighter than the others.

Now the problem was to isolate this coin and find out whether it was lighter or heavier, in five weighings.

How can one do it?

83. Multiplying Bacteria

Bacteria is known to multiply very rapidly.

A certain container contain just one bacteria on the first day and there are twice as many on the next day. In this manner the number of bacteria in the container doubles itself everyday.

Assuming that the container would be full of bacteria on the 10^{th} day, on which day would the container be half full.

84. What a Coincidence!

A group of seven young men named Arun, Binoy, Chunder, Dev, Edward, Fakruddin and Govind were recently engaged in a game. They had agreed that whenever a player won a game he should double the money of each of the other players just as much money as they had already in their pockets.

In all they played seven games and, strangely, each won a game in turn in the order in which their names are given. But what was even more strange was that when they had finished the game each of the seven young men had exactly the same amount, Rs.32 in his pocket.

Can you find out how much money each person had with him before they began the game?

85. The ldler

Ram Rakhan was well known all around his neighbourhood for being a very lazy person. So when he want around looking for a job as a farm-hand everyone refused of engage him, expect farmer Gulab Singh, who was a very smart person.

Gulab Singh engaged the service of Ram Rakhan at a salary of Rs.240 a month consisting of 30 days. However, he set a condition that he would forefeit Rs.10 for each day that he idled. Ram Rakhan accepted the job.

At the end of the month it was found that neither owned the other anything. This taught a lesson to Ram Rakhan.

Can you tell just how many days Ram Rakhan worked and how many days he idled?

86. Numbers Game

During one of my tour to Canada, I came across a very interesting game participated by two players.

A group of match sticks in placed on the table and then it is reduced in my turn by each player by removing from the group at least 1 but not more than 4 match sticks.

The player who takes the last match stick is the winner.

If there is a group of 17 match sticks on the table how would you make your first move, if it was your turn and how would you continuo to play to win?

87. A Bargain in Guavas

Recently I bought some guavas at New Market for Rs.1.20. But they were so small that I made the vendor throw in two extra guavas for the same price.

As I began to walk away the vendor mumbled that this transaction had made him lose 10 paise a dozen less than the price settled before.

How many guavas did I get for my Rs.1.20?

88. The Mathematical Shepherd

Shepherd Gopal had a curious aptitude for mathematics and he was known around where he lived as the ‘Counting Shepherd’.

A man passing through the meadow one day saw Gopal grazing a number of sheep and in the course of a short conversion asked him how many of the grazing sheep were his own. Gopal’s reply absolutely baffled him, which was as follows:

‘ If you divided my sheep into two different parts, the difference between the two numbers will be the same as the difference between their squares. Now figure it out for yourself the number of sheep I own.’

Can you say just how many sheep Gopal had?

89. Father and Son

A father, I know, is 4 times his son’s age. And in 30 years son’s age will be half of his father’s age.

How old are the father and son now?