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 i...

 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.  L...

 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?