Maths Puzzles

 Have not posted here for a long time. Been not busy and idling away.   Here is a simple number puzzle.  Use the numbers 1, 9, 9 and 6 in exactly that order to make the following number.  28, 32, 35, 72, 100 and 1000. You can use the following operators. + - X / √, ^ (exponent symbol).   The question is borrowed from  the site mathisfun.com                  You can find the solution in this post .  

Image from: Popular Mechanics By now you might have heard many, many, many puzzles of some people always telling truth, and others always telling lies. But in real life, we all neither knights, nor knaves. Anyway this puzzle is slightly different - there are couples and these couples both lie or both tell truth or one lies and other one tells truth. (We all like to believe ourselves to be the last one - wink wink) Dags, Eggs and Fens are being interrogated as one of them is a spy. One of the couples always tells truth. In another couple, both husband and wife always lie. And in the third couple, one of the spouses always lies and the other one always tells truth. Here are the statements by the three couples when interrogated. Mr. Dag:  I am not the spy Mrs. Dag:  Mr. Egg is the spy. Mr. Egg:  Mr. Dag is truthful. Mrs. Egg:  Mr. Fen is the spy. Mr. Fen:  I am not the spy. Mrs. Fen: Mr. Dag is the spy.     Which person is a spy? (This puzzle is take...

   In a certain bank the positions of teller, manager and cashier are held by Jones, Smith and Brown, but not necessarily respectively.  The teller is the only child and he earns the least. Smith is married to Brown's sister and he earns more than the manager.  What position does each man hold? (This puzzle is from the book 101 puzzles in thought and logic by C.R.Wylie)    Show answer   Solution : As teller is the only child - Brown can't be teller. Teller earns the least, so teller can't be Smith as Smith earns more than manager.  So teller has to be Jones. Because Smith earns more than manager, Smith can't be manager. And he can't be teller as Jones is teller. So Smith must be cashier.  Brown who is the only one remaining should be manager.  

An artist has a strange idea that a canvas looks good only if its perimeter is equal to its area. Now the question is how many such rectangles are there with integer sides - rectangles with their perimeter equal to their area? And why?  Show answer Solution :  Area = l * w Perimeter = 2l+2w area = perimter => l*w = 2l+2w Moving 2l+2w to left hand side, we get 2l+2w+l*w = 0 Adding 4 to both sides we get=> -2l-2w + lw+4 = 4 => (l-2)(w-2) = 4 The integer pairs with 4 as product are  (1,4),(2,2),(4-1) If l-2 = 1 and w-2=4, we get l = 3 and w = 6 If l-2 = 2 and w-2 = 2, we get l = 4 and w = 4 If l-2 = 4 and w-2 = 1, we again get l = 6 and w = 4 Solutions 1 and 3 are identical. So the only two rectangles with integers sides and area and perimeter being equal are rectangles with sides 3 and 6 and 4 and 4.  

A magician standing next to a bridge offers to double the money to a man each time he crosses the bridge. But he also charges 40$ for crossing the bridge. The man happily agrees and keeps crossing the bridge again and again.  But sadly after the third time he crossed the bridge, the man notices that he has only 40$ left in his pocket which he has to give to the magician. How much money did the man have originally? Show Answer  Answer : 35 dollars. He had 35 dollars and the magician gave him 70  dollars after crossing the bridge. The man gave him 40$ as crossing fee. Now he has 30 dollars. After he crossed the bridge, the magician gave him 60 dollars out of which man gave the magician 40 dollars.  Now he has only 20 dollars left and when he crossed the bridge third time, magician gave him 40 dollars and man had to give all of it to magician.  

To the fraction 1/3, if you add 3 to both its numerator and denominator, its value doubles - it becomes 4/6 = 2/3. Find a fraction whose value triples when you add its denominator to both numerator and denominator.  Find also the fraction whose value quadruples when you add the denominator to its numerator and denominator. Show Answer Answer : 1/5 and 1/7 If we have any fraction with odd denominator 2n-1 and 1 as numerator, when we add the denominator to both numerator and denominator, its value is multiplied by n.  So for n=3, the fraction is 1/2X3-1 = 1/5 and when we add 5 to both numerator and denominator, we get 6/10 = 3/5 Which is 3 times 1/5