Maths Puzzles

 Solution to puzzle 15:  There were 1 cat, 1 dog and 1 fish. So all but two were cats. All but two were dogs and all but 2 were fish. Puzzle 16 The product of age of 3 sisters is 175. Two of the sisters is twins. What is the age of third girl? 

Solution to puzzle 14 Huh, sending more money would have been much easier than this puzzle.      SEND     MORE   MONEY We have to find values for S,E,N,D,M,O,R,Y (8 digits out of 10).  Now, we're adding two 4-digits numbers.  Since 9999+9999 < 20000, M cannot be >=2. And by the "usual rules" for this kind of question, it can't be 0. So M=1 . Now, looking at the fourth (left-most) column, we have either S+1>=10 (if there's no carry) or 1+S+1>=10 (if there's carry). So S=8 or 9 , and O=0 or 1 . Since 1 is already taken, O=0   In the third column, we can't have E+0=N (no carry), so E+1=N and there's carry from the second column.   So in the second column either N+R=10+E=9+N, and R=9, or there's carry and 1+N+R=10+E=9+N, and R=8. So R=8 or 9 , just like S. IF S=8 and R=9,we're looking at 8END + 109E ====== 10NEY But this cannot possibly work: we need to get either E+0=10+N or 1+E+0=10+N in the third column, to get

 I have a confession to make. I chewed more than I can solve. Puzzle 13 - Alibaba‘s cave involves linear programming which I did not study. So I am not very clear about the solution. But my brainy readers can visit this site where in the comments,  various people have solved it,   Puzzle 14: Send more money Yes, isn’t that all our kids used to say? Miss those days.  Now as this is a puzzle and doesn’t involve our family drama, each of the letters in the below sum represent a digit and the sum is correct.       SEND +      MORE ————    MONEY Can you find what are the values of each of the letters S, E etc?

Solution to puzzle 12: I am using brute force algorithm here. Let us start from the divisibility of 5. If two cards remain after dealing them for 5, the largest value less than 52 will be 47 If there are 47 cards and they are dealt to 3 people, 2 cards are left If they are dealt to 4 people 47 - 44 = 3 cards are left So 47 is the correct answer. Puzzle 13 : Alibaba's cave This puzzle is from mrbartonmaths Ali Baba found a cave full of gold and diamonds. A bag full of gold weighs 200 kilograms, a bag full of diamonds weighs 40 kilograms. Ali Baba can carry only 100 kilograms at a time. A kilogram of gold costs $20, and a kilogram of diamonds costs $60. What is the greatest amount of money Ali Baba can earn for the gold and diamonds he can carry out at once (in one attempt in one bag)?

 Solution to puzzle 11: The monk will light both ends of one incense stick and one end of second incense stick. By 30 minutes, first stick will completely burn out and second stick will burn out half. Now the monk will light the other end of second stick. Now the second stick will burn in half the time of 30 minutes. That is, it will burn out in another 15 minutes.  By the times both sticks burn out, it will be 45 minutes. Puzzle 12 : Cards, cards This puzzle is from readers digest. A small number of cards has been lost from a complete pack. If I deal among four people, three cards remain. If I deal among three people, two remain and if I deal among five people, two cards remain. How many cards are there? Guessing game  Before I close this post, I will show you a guessing game. Guess any number. Now double the number. Add 10 to it. Next halve the number. Subtract original number from it. Now your answer is 5. Is it not?  So, how do people do that? Simple.  Let us say original numbe

 Solution to puzzle 10: Farmer first takes the hen and crosses the river. Leaves the hen there.  Next he comes back and carries the fox and crosses the river.  He leaves the fox and brings back hen.  Next he leaves hen behind and takes corn and crosses the river and leaves the corn along with fox.  Lastly he goes back and brings hen and crosses the river. Puzzle 11 : Meditation A monk is asked to meditate exactly for 45 minutes in a room which has nothing but 2 incense sticks and matches. Each of these sticks burn exactly for 1 hour but at diffère rates. He is not allowed to break the sticks. How will he use the two incense sticks to measure 45 minutes? 

  Solution to puzzle 9 There must be a coin with value 5. Because to represent number 10 with maximum of 2 coins we need a coin of 5 There must also be coin of value 1 to represent number 1.  To represent 9, we also need a coin of value 4 along with a coin of value 5. So we must have coins of 1, 4, 5.  Now to represent 3, we can either have a coin of 3 or two coins of 1 and 2.  So the two possible answers are 1,2,4 and 5.  And 1,3, 4 and 5.  With 1 2 4 5 1 -1 2-2 3 - 1 2 4 - 4 5 - 5 6 - 1 5  7 - 2 5 8 - 4 4 9 - 4 5 10 - 5 5 You will also find such a representation for 1 3 4 5 Puzzle 10: A hen, a fox and a corn This puzzle and it’s various versions are as old as me. It is no exactly a mathematical puzzle but a logical one.  A farmer has to take a hen, a fox, and some corn across a river. The farmer can only take one thing across at a time. Unless the farmer's present the fox will eat the hen and the hen eat the corn. How is it done? 

 Solution to puzzle 8: Maria is not counting Sundays. So she is not counting 1/7th of days of her age.  That is to say she is only counting 6/7th of her age. 6/7th of her age = 30 Her actual age = 30 X 7/6 = 210/6 = 35 years.  Puzzle 9 : The 4 coins problem  You’re creating a new coin system for your country. You must use only four coin values and you must be able to create the values 1 through 10 using one coin at a minimum and two coins maximum. What 4 coins do you choose, and can you think of a second set of 4 coins that achieves the same goal?

 Solution to puzzle 7: Let us say the cost of ball is x. Then cost of bat is 1+x. Both together costs 1.10 Rs. x+(x+1) = 1.1 2x+1= 1.1 2x = 1.1 -1 =0.1 x = 0.05 So the ball costs 5 paise. And bat costs 1 rupee and 5 paise.  Puzzle 8 : Nice try  Maria never told her correct age. She subtracted Sundays when mentioning her age as according to her she does not work on Sundays. She tells her age is 30 years. What is her actual age?

 Answer to puzzle 6: There are various combinations of water pouring puzzle. This I think is the simplest one. You need to measure exactly 2 liters using jugs do 5 liter and 3 liter capacity.  You fill the 5 liter jug completely. Next from that jug, you pour 3 liter of water into 3 liter jug. Now the bigger jug has exactly 2 liter of water in it. Quite easy, don’t you agree? Puzzle 7: Bat and ball The cost of a bat and ball together is 1.10 rupees. Bat costs one rupee more than the ball. What are the prices of bat and ball? P.S.   I hear you ridiculing me, how on earth can the cost of anything be 1.10 rs. The puzzle was using British pound as currency. I being as patriotic as the next woman, changed it to Indian rupees.

 Solution to puzzle 5: Let us say goat ate x kgs of wheat.  Horse eats twice as much as goat => horse ate 2x kgs of wheat. Cow eats twice as much as horse => cow ate 4x kgs of wheat Total wheat eaten by all 3= 5kgs Which means x+2x+4x = 5 7x = 5 x = 5/7 Goat's owner has to get give 5/7 kgs of wheat to the farmer Horse ate 2x = 10/7 kgs of wheat. So owner of horse must give 1 3/7 kgs of wheat to the farmer. Cow ate 4x = 20/7 = 2 6/7 kgs of wheat. So owner of cow must give 2 6/7 kgs of wheat to the farmer .  Puzzle 6: Water pouring puzzle  You are given two jugs which can hold 5 liters and 3 liters of water. The jugs do not have any markings on them. You also have access to a water tap from which you can pour as much water as you want. How will measure 2 liters of water using only these two jugs?

Solution to Puzzle 4:  The solution to puzzle 4 was much more complicated than I imagined. My google gave many solutions. I liked this solution from Nytimes better. I am copying and pasting from nytimes            Number the coins 1 through 12. First weighing: 1,2,3,4 v 5,6,7,8. If equal, weigh 9,10,11 v 1,2,3 (not counterfeit). If equal, 12 is the counterfeit and weigh it against any other coin to determine if it’s heavy or light.  If not equal, the direction of 9,10,11 will determine heavy or light.  The third weighing is 9v10.  If equal, 11 is counterfeit.  If not, which ever of 9 or 10 went the same direction as in the second weighing is counterfeit (and you’ll know heavy or light from the second weighing). If 1,2,3,4 v 5,6,7,8 is not equal, mark which way each side moved.  Let’s assume 1,2,3,4 went down and 5,6,7,8 went up.  The second weighing is 1,2,5 v 3,4,6 where three of the coins change sides.  If equal either 7 or 8 is counterfeit so weigh them against each other

 Answer to Puzzle 3: You select to go first. First you pick 9 candies so that 96 candies are first. After Patrick picks up his share of candies, you pick candies so that there are 90 candies left in the pile. e.g. If he picks up 1 candy, there will be 95 candies - and you pick 5 candies. If he has picked up 2 candies, you pick up 4 candies If he picks up 3 candies, you pick up 3. So now you get the idea.   Now there are 90 candies, he will pick up 1/2/3/4/5 candies and you pick up so that there are 84 candies left in the pile. Each time, you select a number so that the pile will have a multiple of 6 candies. In the penultimate round, you pick up candies leaving behind 6 candies. No matter how many candies Patrick picks up, there will be 1/2/3/4/5 candies left in the pile. So you pick them up and you have won your mint candy!   ಒಗಟು ೪ - ಖೋಟಾ ಸಿಕ್ಕಾ : ನಿಮ್ಮ ಹತ್ತಿರ ನಿಮ್ಮ ಮುತ್ತಜ್ಜಿಯ ಸಂಗ್ರಹದ ೧೨ ನಾಣ್ಯಗಳಿವೆ. ನಿಮ್ಮ ಅಜ್ಜಿಯ ಪ್ರಕಾರ ಅವುಗಳಲ್ಲಿ ಒಂದು ನಾಣ್ಯ ಖೋಟಾ ನಾಣ್ಯ. ಆ ನಾಣ್ಯ ಬೇರೆ ನಾಣ್ಯಗಳಿಗಿಂತ ಭಾರವಾಗ

 Solution to puzzle 2: There is no missing dollar.  The lawyers paid 30 dollars to the hotel of which they got back 5 dollars. Which means they paid 25 dollars to the hotel. And they paid 2 dollars to the waiter as tip. So the total amount they spent is 25+2 = 27 dollars. They each had paid 10 dollars initially and they got back one dollar each. Which means they each spent 9 dollars. 9 X 3 = 27 dollars.  Balanced!! Puzzle 3 : A sweet treat  You and Patrick have a candy competition. There is a pile of 100 caramel candies and one mint candy. Each of you have to take minimum 1 and not more than 5 candies at a time. The person who gets to pick up last candies will have mint candy as a prize which you love very much.   Patrick has let you decide who goes first.  Now who should be the first one to pick candies in order for you to win the race?   Hint : Try with 10 candies at first.  

 Solution to puzzle 1:          100 64 and 16. Puzzle 2: Three lawyers check into a hotel room and pay 30$ rent for the day - 10$ each per person. A waiter comes and tells them that they have won a discount offer and the total rent is only 25$ now. He returns 5$.   The lawyers decide to keep 1$ each and give 2$ as tip to the waiter. So the total was 9X3 +2 = 29. They can’t understand where is the missing dollar. Can you help them? 

Here is an interesting but simple geometry puzzle. We have a triangle. And this triangle has all squares.  The 3 angles of this triangle are  all square numbers. That is x, y and z shown in the image below are square numbers.  Can you find out the values of these angles? Hint : Sum of angles of a triangle are 180