Maths Puzzles

 The puzzle was to get the numbers 28, 32, 35, 72, 100 and 1000 using the digits 1,9,9, 6 in exactly the same order.  You can use the following operators -  + - x  / and also √ and ^      Here is the solution 28 = 1+ 9x (9-6)  32 =  1/  √9 x (96) 35 = -19 + 9x6 72 =( 1+  √9 ) x  √ 9 x 6 100 = 1 +  √ 9 + 96 1000 = (1+9)    ^ (9-6)        

Number Puzzle Medium Can You Solve This Tricky Maths Puzzle?  Use the numbers 1, 9, 9 and 6 in exactly that order to make the following numbers-   28, 32, 35, 72, 100 and 1000  You can use the following operators. + - X / √, ^ (exponent symbol).  💡 HINT Remember the order of mathematical operations. The question is borrowed from  the site mathisfun.com     ✓ SOLUTION Step-by-step explanation: 8 + 8 ÷ 2 × 4

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 the reason 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

This puzzle is from "The Moscow Puzzles" by Boris Kodemsky is from another era - when there were things like clocks which need to be wound each day. If not they would stop. The puzzle goes like this. I have a wall clock which is the only source for knowing the time in my house. One day I forgot to wind the clock and it stopped. Luckily, I have a friend whose clock shows the correct time always.  I walk down to his house, see the time in his clock, stay for a while and come back. Now I know the time and adjust my clock. It is is showing the correct time again.  How did I do that?   Show Answer Answer: I wind up the clock before leaving the house and set it at 12 o'clock. It starts running. When I go to my friend's house I notice the time. And just before leaving the house, I also see the time. When I come back, I see the time on my clock. That will show the total time elapsed since I left home. Now since I know the time in my friend's house as soo...

 There are 7 matches arranged in the form of a star. Your aim is to place 6 coins at the head of 6 of the matches. You should start from a match which does not have a coin at the end, count and place a coin at the third match. You should not skip any match while counting. Can you arrange the coins this way without placing two coins at the head of any match? (This puzzle is also taken from the book "The Moscow Puzzles" by Boris Kordemsky)   Show Answer Answer: Start by choosing any matchstick—let us say A—and place a coin on the third matchstick counting from A. Next, select another matchstick—let us say B—so that A becomes the third matchstick when counting from B, and place a coin on A. Then choose a new starting matchstick so that B is the third matchstick from it, and place a coin on B. Continue this process, and you will place all the six coins.

There are three piles of match sticks with 11 matches, 6 matches and 7 matches in them. Now you need to move the matches from one pile to another pile such that all of them have 8 matches each.  But there is a condition - you can add as many matches to a pile as it already contains. For example if a pile has 3 matches, you can add only 3 matches to it - no more, no less.  You are allowed such three moves. How will you move the matches? (The puzzle is borrowed from the book "The Moscow Puzzles" by Boris Kordemsky)  Show answer Answer : First you move 7 matches from first pile and add it to the last pile.  Now you have 4 - 6 - 14 matches in the piles Next you move 6 matches from last pile to middle pile. Now you have 4 - 12 - 8 matches in the three piles. Lastly you move 4 matches from middle pile to first pile.  You have 8 - 8 - 8 matches in the piles.  

 On a table, 3 normal playing cards are placed face down.  To the right of a king, there is a queen or queens. To the left of a queen there is a queen or queens.  To the left of a heart, there is a spade or spades.  To the right of a spade, there is a spade or spades.  Which three cards are on the table? (Borrowed from the book "The colossal book of short puzzles and problems" by Martin Gardner)  Show answer The first rule says that there is atleast one king. Second rule says that there are two queens. (KQQ,QKQ) Third rule says that there is a heart and a spade. And the fourth rule says that there are two spades. (HSS,SHS,SSH) Which means out of three cards, two are queens and one is king. And two are spades and one is hearts. So the four possibilities are   KS, QS, QH KS, QH, QS QS, KS, QH QS, KH, QS The fourth is an impossible option as there can't be two queen of spades in a deck. So the three possible answers are  King of s...

A scale is balanced. On one side of the scale, there are 3 1 ⁄ 2 bags of rice and on the other side there are 1 3 ⁄ 4 bags of rice and 1 ⁄ 4 kilo weight. What is the weight of one bag of rice? This puzzle is borrowed from the book "Brain teasers" by Ian Livingstone and Jamie Thomson Show answer Let the weight of 1 bag of rice be b. So 3 1 ⁄ 2 b = 1 3 ⁄ 4 b + 1 ⁄ 4 Transferring  1 3 ⁄ 4 b to LHS we get 1 3 ⁄ 4 b =   1 ⁄ 4   b =  1 ⁄ 4  /  1 3 ⁄ 4 =    1 ⁄ 7 kg

  Can you add two to eleven and get one as the answer? How?   Show answer Answer : When you add 2 hours to 11 o'clock, you get one o'clock.    The question is borrowed from the book "Brain teasers" by Ian Livingstone and Jamie Thomson.

A bag contains some red pencils and some blue pencils. The ratio of red to blue pencils is 7:11. If the total number of pencils the bag is 90, what is the number of blue pencils? (This question is borrowed from the book "Competitive Maths for middle school" by Vinod Krishnamoorthy)  Show answer Answer : 55 pencils   If the total number of pencils is 7+11 = 18, then 11 is the number of blue pencils. So the ratio of blue to total is 11:18   Since the total number of pencils is 90, number of blue pencils is 11/18*90 = 55 pencils

There are 5 consecutive even numbers whose sum is 640. Which are these numbers? e.g. 2,4,6,8,10 are consecutive even numbers and their sum is 30. Show answer The average of 5 consecutive even numbers will be equal to the third number. Because if the numbers are x,x+2,x+4,x+6,x+8, then their sum is 5x+2+4+6+8 = 5x+20 Their average is (5x+20)/5 = x+4 which is the third number of the sequence. Here the sum is 640 => average is 640/5 = 128 Hence the sequence is 124,126,128,130,132

An explorer Dr. Franz was trekking across a desert in search of a secret treasure. But the water container in his jeep was leaky.  In the first hour, the container lost half of the water plus one litre. In the second hour it again lost half of the remaining water plus one litre. In the third and fourth hour same thing repeated. But by the end of fourth hour, the container was empty. How much water did the container originally hold?   Show answer Answer = 30 liters   Let us say there was x liters of water to start with.  First hour he lost x/2 liters +1  First hour remaining water was x - (x/2+1) = x/2 - 1   Second hour he lost (x/2-1)/2  + 1 = x/4 -1/2+1 = x/4 +1/2 Second hour remaining water was x/2 -1 - (x/4 +1/2) = x/4 - 3/2   Third hour he lost( x/4 - 3/2 )/2 +1 = x/8 +1/4 Third hour, the remaining water was x/4 - 3/2 - x/8-1/4 = x/8 - 7/4   Fourth hour he lost (x/8 - 7/4)/2 +1 = x/16- 7/8 + 1 = x/16 + 1/8 Fourth hour, the remaining ...

 Answer is 35 Let us use first letters of their names as number of drones shot by each pilot. I = 10+J ------(1) L = I - 4 ------(2)    => L = 6+J J + V = 9 ------(3) L = 3+V------(4).   =>6+J =3+V => V - J = 3 V  =  C + 2 ------(5)    V+J = 9 V-J = 3  Adding these two, we get 2V = 12   => V = 6.  and J = 3   L = 6+J = 9 I = 10+J = 13 C = V - 2 = 4 Total number drones shot down is sum of all these= I+J+L+V+C = 13+3+9+6+4=35     

This puzzle is from the book "Brain teasers" by Ian Livingstone and Jamie Thomson. Earth was under attack by marauding Mechanoids—robotic machine aliens from  another world. Five Earth Force pilots returned from a sortie into space after destroying several Mechanoid Battle Drones.    Ibrahim shot down 10 more than  Juan. Luke shot down 4 less than Ibrahim. Juan and Vladimir shot down 9  between them. Vladimir shot down 2 more than Chi, but Luke shot down 3 more  than Vladimir.   How many Battle Drones were shot down in all?     You can find the solution here .  

 It is not. Because your wife is widow, only if you are dead. A dead man can't marry. The man is living in the ground floor of a high rise building. So even when he jumps out of his window, he has not fallen down from a height and is perfectly fine. The man has entered a lift and has pressed a button to go down. When the lift is going down, his weight is temporarily reduced due to the downward motion of the lift. And when the lift stops and man gets out of the lift, he has his original weight.  

Is it legal in India for a man to marry his widow's sister? Justify your answer. A man living in a high rise building decides one day to go out of the window instead of door. He jumps from the window. But he survives the fall without a scratch, and continues to walk to his office. How is this possible? A man enters a room and presses a button. Immediately he is 10 kg lighter. However when he leaves the room, he is having his original weight. How?      Find the solutions here .