Mathematical & Logical Puzzles -Q3

9.   The Weights And The Scales

            A shopkeeper has a beam balance and requires to weigh any article of a whole number of grams from 1 to 40 inclusive.  What is the least number of weights necessary to do this?

 

10. The Efficient Electrician

            An electrician is faced with the following annoying dilemma.  In the basement of a three-storey house he finds, bunched together in a hole in the wall, the exposed ends of eleven wires, but he has no way of knowing which end above belongs to which end below.  His problem is to match ends.

            To accomplish his task, he may do one of two things:

·      Short circuit the wires at either end by twisting the ends together in any manner he chooses.

·      Test for continuity of a closed circuit by means of a “continuity tester”, consisting of a battery and a bell.  The bell rings when the instrument is connected to two ends of a continuous unbroken circuit.

            Not wishing to exhaust himself with needless stair climbing and having a passionate interest in operations research, the electrician sat down on the top floor with a paper and pencil and soon devised the most efficient method of labelling the wires.  What was his method?

11. How Old Are You?

            Mr. Jones said to Mr. Smith:  “When I was as old as you are now, you were twice as old as you were when I was three times as old as you.”  How old is Mr. Jones if Mr. Smith is 28?

12. Ann And Mary

            The present sum of the ages of the two girls is 44.  Mary is twice as old as Ann was when Mary was half as old as Ann will be when she is three times as old as Mary was when she was three times as old as Ann.  How old are Ann and Mary?


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