Maths Puzzles

A go cart track is 1 mile long. A driver drives the cart at a speed of 30 miles an hour in the first lap. What must be his speed in the second lap, so that he completes the two laps in two minutes?

 Here is the solution to puzzle 76      2 + 4 X 6 + 8 = 44      2 X 4 - 6 + 8 = 16      (2 + 4) / 6 + 8 = 9  

What arithmetic symbols do you have to insert in between the numbers to get the correct result? Note that only the symbols +, -, × , ÷ and () are used. 2 4 6 8 = 44 2 4 6 8 = 16 2 4 6 8 = 9

 Here is the solution to puzzle 75  Well, it is actually very simple. The first digit of previous number is moved to last. The series was 4782, 7824, 8247   So the next number is 2478.

 What number comes next in the series?          4782, 7824, 8247,-----?

 Here were some simple puzzles The solutions are as follows The numbers whose product  = their sum are 1,2 and 3. Do you know any more sets? There are 3 books to the left of the given book and 8 to the right. So totally 3+8+1 = 12 books are there.  99 + 9/9 = 100. If you like to arrange numbers to get a target number, have a look at my countdown game Of course, he was born on 29th of February and his birthday arrived only once in 4 years.

 Or shall I say slightly silly? Which three positive integers have their sum equal to their product? There are several books in a book shelf. If a book is 4th book from the left and 9th book from the right, how many books are there totally? Can you arrange four 9s to make it a 100? A very old man dies on his 25th birthday? How is the statement correct? You may know all the 4 answers as these are quite commonly asked riddles and not at all tough.

The product of all the numbers in your telephone is    0 Because the phone has a zero in it. When you multiply any number by 0, you get 0.

 Do you know the sum of 1+2+3+....+1000=? How fast can you find out the sum?  OK, let us go in steps. How much is 1+2+3+..+10? Is it 55? Did you add all the numbers? Really? Did you add all the numbers?  Then certainly you can't find out sum of all the numbers from 1 to 1000. You will be bored to death before you finish adding them. The formula my dear is 1+2+...+n = n(n+1)/2 You already knew it? You are the smart one! Aren't you? OK. Now for the real puzzle of today. What is product you get when you multiply all the numbers on your telephone?  (You must have seen a telephone, a landline telephone? Even if you haven't, what is the product of numbers on your mobile, when you try to dial some number - product of all numbers on the the numeric keypad. Excluding backspace and hash. We are not into cryptography - yet!)

 Here is a set of silly puzzles. I am the beginning of sorrow and the end of sickness. You cannot express happiness without me yet. I am always in risk yet never in danger. You may find me in the sun, but I am never out of darkness. Paul’s height is six feet, he’s an assistant at a butcher’s shop, and wears size 9 shoes. What does he weigh? A man is looking at a photograph of someone. His friend asks who it is. The man replies, “Brothers and sisters, I have none. But that man’s father is my father’s son.” Who was in the photograph? The person who makes it has no need for it. The person who purchases it does not use it. The person who does use it does not know he or she is. What is it? The water level in a reservoir is low, but doubles every day. It takes 60 days to fill the reservoir. How long does it take for the reservoir to become half full?   Solutions The letter s. He weighs meat. Ha ha. His son. A coffin 59 days. Because if it is half full on 59th day, it will...

  The question was The following characteristics apply to a group of people in a room: Fourteen are blonds, eight are blue-eyed, and two are neither blond nor blue-eyed. If five of the people are blue-eyed blonds, how many people are in the room?   Solution :   Let us try to understand this with a diagram In this diagram a = blue eyed people who are not blond     b - blond people who are not blue eyed c - both blond and blue eyed      d - neither blond nor blue eyed (which is 2) We know that c = 5. And a+c (blue eyed people)= 8. Which means a  = 8-5 = 3 We also know that b+c = number of blonds  = 14. So b = 14 - 5 = 9 Now total number of people in the party  = a+ b+c+d = 3+9+5+2 = 19 So c is the correct answer.

 The following characteristics apply to a group of people in a room:  Fourteen are blonds, eight are blue-eyed, and two are neither blond nor blue-eyed. If five of the people are blue-eyed blonds, how many people are in the room? (a) 3 (b) 17 (c) 19 (d) 24 (e) 29  

 The puzzle is A car goes uphill a certain distance at a speed of A km per hour. Then it comes back the same distance at a speed of B km per hour. A and B are not equal.  Which of the averages are greater - Average of A and B or average speed of the total travel?  The answer is average of A and B. Solution :    Let us say the distance the car travels in one direction is D. Let the time taken for uphill travel is t1 and time taken for downhill travel is t2. Total distance traveled = 2D Total time = t1+t2 = D/A + D/B = DB+DA / AB = D (A+B)/AB Average speed of the travel = distance / time = 2D /(D (A+B) / AB)                     = 2AB/(A+B)    Average of A and B  = (A+B)/2 Which of these two is greater? 2AB/(A+B)                     A+B / 2 2AB       ...

A car goes uphill a certain distance at a speed of A km per hour. Then it comes back the same distance at a speed of B km per hour. A and B are not equal.  Which of the averages are greater - Average of A and B or average speed of the total travel?

 The question was  What is wrong with this proof ? a=b multiply both the sides by a     --1 a2 = ab  add -b2 to both the side           --2 a2-b2 =ab-b2  factorizing                                --3 (a+b)(a-b) = b(a-b)  divide both the sides by (a-b)    ---4 a+b=b Substituting a with b,              ---5 2b = b Dividing both the sides by b    ---6 2 = 1   The problem is with step 4. When a is equal to b, a-b is zero. You can not divide numbers by zero because division is only defined for non-zero numbers.  

 The puzzle was   The sum of two numbers is 10. The product of these numbers is 20. What is the sum of their reciprocals? Instead of writing complicated equations, we can use a simple tweak.  If the numbers are x and y, then sum of their reciprocal is 1/x+1/y = (x+y)/xy Since we have both sum - x+y and product - xy of the numbers, the answer is 10/20 = 1/2

The question was In the following subtraction problem, each letter uniquely repre- sents one digit from 0 to 9. At least one digit is not 0. Find the values of A, B, and C. ABA – CA= AB  Now if A, B and C represent digits from 0 to 9, the following equation will be 100A+10B+A - (10C+A) = 10xA+B  90A+9B = 10C  9(10A+B) = 10C 10A+B = 10/9 C  To have integer values for A and B, C has to be 9. By replacing C with 9 we get, 10A+B = 10 If A and B have to between 0 to 9, A has to be 1 and B has to be 0. So A =1, B = 0 and C=9  

In the following subtraction problem, each letter uniquely represents one digit from 0 to 9. At least one digit is not 0. Find the values of A, B, and C.   ABA  –      CA -------------      AB

 The sum of two numbers is 10. The product of these numbers is 20. What is the sum of their reciprocals?

 The question was   A train is travelling at the speed of 96 kilometres per hour. It takes 3 seconds to enter a tunnel and 30 seconds more to pass through it completely. What is the length of the train and the tunnel?   Solution:       Time taken for the entire train(from front to rear) to enter the tunnel (from front to rear) = 3 seconds       Distance traveled in 3 seconds = 3 X 96X1000/(60X60) meters = 80 meters       80 meters is the length of the train           Time taken for train to pass through the tunnel = 30 seconds.         Distance travelled in 30 seconds = 30 X 96X1000/(60X60) meters = 800 meters         Length of the tunnel = 800 meters.

  A train is travelling at the speed of 96 kilometres per hour. It takes 3 seconds to enter a tunnel and 30 seconds more to pass through it completely. What is the length of the train and the tunnel?

 This puzzle is from the book by world famous Shakuntala Devi What is wrong with this proof ? a=b multiply both the sides by a a2 = ab  add -b2 to both the side a2-b2 =ab-b2  factorizing (a+b)(a-b) = b(a-b)  divide both the sides by (a-b) a+b=b Substituting a with b, 2b = b  2=1

 The quiz was  Terry is half as old as Alice was when Alice was 5 years old than Terry is now. What is Terry's age now? Solution:  alice then = terry+5 terry = alice then /2 = (terry+5)/2  2 terry = terry+5 terry = 5.  

 Convoluted! That is what this puzzle is. Just like the talk of bureaucrats. Terry is half as old as Alice was when Alice was 5 years older than Terry is now. What is Terry's age now?

 The puzzle was   Anthony and Cleopatra are lying dead on the floor of a villa in Egypt. Nearby is a broken bowl. There is no mark on either of their bodies and they were not poisoned. How did they die? And the answer is - Anthony and Cleopatra are not the queens and kings of Egypt. They are fish. They died because the bowl of water in which they were residing broke.  It is silly. But we like silly too . 

 The question was  In a certain bank the position of cashier, manager and teller are held by Brown, Jones and Smith, though not necessarily respectively. The teller, who was an only child, earns the least. Smith who married with Brown’s sister, earns more than the manager As the teller is the only child he can't be Brown - Brown has a sister. He can't be Smith either because Smith earns more than the manager. So teller has to be Jones. Smith earns more than the manager - and he can't be manager or teller. Smith has to be cashier. Now only one left is Brown. He is the manager. Very simple. And we like simple!

This one is kind of silly. Of course I liked it. You will too.   Anthony and Cleopatra are lying dead on the floor of a villa in Egypt. Nearby is a broken bowl. There is no mark on either of their bodies and they were not poisoned. How did they die?

 Normally the logic puzzles will be too convoluted to even understand. But this one is not.  In a certain bank the position of cashier, manager and teller are held by Brown, Jones and Smith, though not necessarily respectively. The teller, who was an only child, earns the least. Smith who married with Brown’s sister, earns more than the manager Can you find out which post is held by who?

 A man left legacies to his 3 sons and a hospital. The total amount of his legacy was $1320. If he had left the hospital legacy to his first son, he would have received as much as other two sons together. If he had left the hospital legacy to his second son, he would have received twice as much as the other two sons together. If he had left the hospital legacy to his third son, he would have received thrice as much as the other two sons together. Find the amount of each legacy.  Solution: Let the legacies of first, second and third sons be x,y and z respectively. Let h be the legacy of the hospital. Given x+y+z+h = 1320 x+h = y+z y+h = 2* (x+z) z+h = 3*(x+y) Replacing h with 1320-x-y-z, we get the equations as x+1320-x-y-z = y+z y+1320-x-y-z = 2*(x+z) z+1320-x-y-z = 3*(x+y) Simplifying and solving we get x = 55, y = 275 and z = 385. And h = 605

 Here was the question   "When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel's worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a news-paper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?" Solution : Let us use a bottom up approach here.  Mr. Tompkins (funny name!) had a nickel when he reached his destination.  Prior to that he gave 15 cents to a beggar . Before giving money to beggar he had 15+5 = 20 cents. Before that, he spent half his money for bus ticket. Which means  20 = half of what he had Money he had before buying bus ticket = 2*20 = 40 cents  At the time of reaching bus terminal, he had spent half of what he had+10 cen...

 "When I got to the station this morning," said Harold Tompkins, at his club, "I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel's worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a news-paper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?" (By the way 1 nickel is 5 cents and 100 cents is 1 dollar. I googled it)   Find the solution in this post.

  By the way, gold ingot is a gold bar. I googled. This is quite a simple puzzle.  Solution :  Let us say the weight of of ingot is x kg.  On one side of scale is 1 ingot = x kg On the other side is 1/2 ingot and 3/4kg weight = x/2+3/4 As they balance,   x = x/2 + 3/4 Transferring x/2 to LHS, we get  x - x/2 = 3/4  x/2 = 3/4  x = 2* 3/4 = 1.5 kg  

Puzzle 1 : When asked his age, Jack tells that "In 2 years I will be twice as old as I was six years ago" . How old is Jack now? Puzzle 2: James  was  asked how old he is.  James said: “Five years ago my Dad was five times older than me, but now he is only three times older!” How old is James and how old is his father? Solutions :  1. If Jack's age is x, then    x+2 = 2*(x-6)    x+2 = 2x-12 2+12= 2x-x  x = 14 Jack is 14 years old now. 2. If James's age is x and his father's age is y, x*3 = y and  (x-5)*5 = y-5 Substituting y with 3x in the above equation, we get 5x - 25 = (3x) - 5  2x = 25 - 5 = 20 x = 10 and y = 30 So James is 10 years old and his father is 30 years old. 

      Solution: 2 + 4 X 6 + 8 = 44 2 X 4 - 6 + 8 = 16 2 + 4 ÷ 6 + 8 = 9  

 Solution: It is E.  All the other symbols have 2 rectangles, one circle and one line. E has 3 rectangles, one circle and one line.   A simple puzzle : Sharan has five sons and each son has a sister. How many children does Sharan have? Solution : If you guessed 10, I have done the same mistake too. But each son has one sister because there is only one daughter in the family. So Sharan has 5 sons and one daughter. He has 6 children. 

 Solution : There are 5 sheep and only one of them is ewe.  Number of heads = 5    Number of hooves = 20 Number of tongues of ewes = 1 Heads*hooves*tongues = 5*20*1 = 100

Harry owes Sam $30. Sam owes Phil $20. Phil owes Harry $50. Which of the following will settle the debts? Harry could give Phil $50. Sam could give Phil $20 and Harry could give Sam $40. Harry could give Phil $20 and Sam could give Phil $10. Sam and Phil could give Harry $50 total. Phil could give Harry $20 and could give Sam $10. Solution: 5  Harry owes Sam 30 and Sam owes Phil 20. We can say that Harry owes Phil 20. But Phil owes Harry 50. We can subtract 20 which Harry owes Phil. Which means Phil really owes Harry 30. But Harry owes 10 to Sam now (after subtracting 20 of Phil). So Phil can give this 10 to Sam on Harry's behalf and he can give the remaining 20 to Harry.

Solution : Alice and Ben cross the bridge in 2 minutes. Next Alice comes back with the torch in 1 minute. Next Cindy and Don cross the bridge in 8 minutes. Now Ben goes back with the torch in 2 minutes and Ben and Alice come back in 2 minutes.  Total time taken = 2+1+8+2+2 = 15 minutes

In a room, there are 14 people who are blond and 8 people who are blue eyed. Five of these people are both blond and blue eyed. There are also two persons in the room, who are neither blond, nor blue eyed. How many people are in the room?   Solution : 19  There are 14 blonds and 8 blue eyed people. As 5 of these are both blonds and blue eyed,  Number of blonds but not blue eyed = 14-5 =9 Number of blue eyed but not blond = 8 - 5 = 3 Number of blond, eyed people = 5 Number of people who are neither blond, nor blue eyed = 2 So total number of persons in the room = 9+3+5+2 =  19

  Solution : If you take 635 as a, the first product  - a * (a+1) = a 2 +a Second product - (a-1) * (a+3) = a 2 -a+3a-3 = a 2 +2a-3 So second product  - 634*638 is larger.

Solution :The smallest difference is 49 minutes. Between 12:12 and 01:01.

    Solution : Solution is rather silly. Just take the second glass and pour its content to fifth glass and keep back the empty glass. Lo, you have your alternate filled and empty glasses. 

 Solution :  Head of the bird h = 9 Tail of the bird t = h + b/2 where b is size of body Body of the bird b = h+t = h+h+b/2 Transferring b/2 to LHS, we have  b/2 = 2h   =>  b = 4h = 4*9 = 36cm. t = h+b/2 = 9+36/2 = 9+18 = 27 cm. Size of the bird = h+t+b = 9+27 + 36 = 72cm.

  Solution : Wednesday Explanation: Yesterday was Wednesday. Which means today is Thursday.  Thursday Archie tells truth. Which means Archie's statement -'I lied yesterday.' is true. This supports the statement ' Archie lies on Monday, Tuesday and Wednesday and tells truth on other days'. Kent lies on Thursday. So his statement 'I lied yesterday' is a lie. Which means he did not lie on Wednesday. This supports the statement 'Kent lies on Thursday, Friday and Saturday and tells truth on other days' .

  Solution: First and last chests have treasure in them. Explanation : Message 1 says that middle chest has treasure. Since all messages are false, middle chest has no treasre. Message 2 says that all these chests have treasure. Which means at least one of them does not have treasure (and has poison). Which is middle chest. Message 3 says that only one of the chests has treasure. As this is false, more than one of the chests have treasure. As middle one has no treasure, the other two - first and last have treasure.