Published on January 10, 2008
Slide1: Juice You buy a bottle of juice for €1.00. The juice costs 90 cents more than the empty bottle. How much does the empty bottle cost? Slide2: Talia's Giveaway Talia has some money in her pocket. She gives half of the money to Allison. Then she gives 1/4 of what she has left to Lauren. Talia then sees David, and she gives him 1/3 of what she has left. Now you come along, and Talia equally shares the money she has left with you. You get €2! How much money did Talia have to start with? Who gets the most money? Slide3: Who Carries the Rocks? April, Rosa, and Carrie, who are sisters, went on a hike. They found four rocks that they want to bring home to add to their collection. Each girl has a backpack to carry the rocks. In how many different ways can the three sisters take home four rocks in their backpacks? Slide4: Pizza Party Roma Pizzeria offers the following toppings for a standard large pizza: pepperoni, mushrooms, peppers, onions, and sausage. In addition to ordering a plain pizza, you can order any number of toppings, even all five (which happens to be the "special"). How many different kinds of large pizza do you have to choose from? Slide6: Round and Round There is a machine with 2 gear wheels. One wheel has 8 teeth, and the other wheel has 5 teeth. If you turn the large wheel, the teeth make the small wheel turn, but in the other direction. Suppose you turn the wheels so the larger wheel goes around once. The smaller wheel is not back in its starting place. So, you keep turning the wheels until they both get back to their starting places. How many times will each wheel go around? Slide7: Sticks and Squares Which toothpick can you take away to leave three equal squares? Slide8: 100 Wins! Use all the numbers shown, any of the following four operations, +, −, ×, ÷, and parentheses to make a total of 100. 1 2 3 4 5 6 7 8 9 You may not change the order of the numbers, or use them more than once! Slide9: Penny Candy Sonia spent 70¢ buying small sweets at the corner store. She bought some 1¢ sweets, some 2¢ sweets, some 3¢ sweets, some 5¢ sweets, and some 10¢ sweets. She bought 17 sweets altogether, four each of two kinds, three each of the other three kinds. How many candies did she buy at each price? Slide10: Doubling Amoebas Amoebas are one-celled animals that reproduce by dividing in two. One amoeba becomes two, two become four, and so on. If they have enough food, amoebas can double their population every 24 hours. If you start with just one amoeba in a jar of pond water at 10 A.M. on Monday morning, how many amoebas are in the jar by Wednesday of the next week at 10 A.M.? (Assume that none die.) Slide11: To Get to the Other Side Zoe, Claire, and Kristin have to cross a river to visit their friend Tasha. They have a boat, but they also have a problem. Zoe and Claire each weigh 50 kg. Kristin weighs 75 kg, and the boat will carry only 100 kg at a time. “Oh no! We can't all get across the river!” moans Claire. Kristin thinks for a moment and says, “I know a way we can all get across. It will just take more than one trip.” What is Kristin's plan? Slide12: The Bridge A Family of four (father, mother, son, and daughter) went on a hike. They walked all day long and, when evening was already drawing on, came to an old bridge over a deep gully. It was very dark and they had only one lantern with them. The bridge was so narrow and shaky that it could hold no more than two persons at a time. Suppose it takes the son 1 minute to cross the bridge, the daughter 3 minutes, the father 8 minutes, and the mother 10 minutes. Can the entire family cross the bridge in 20 minutes? If so how? (When any two persons cross the bridge, their speed is equal to that of the slower one. Also the lantern must be used while crossing the bridge.) Slide13: Ducky numbers. For many years now Baron Münchhausen has gone to a lake every day to hunt ducks. Starting on August 1, 2000, he says to his cook: "Today I shot more ducks than two days ago, but fewer than a week ago." For how many days can the baron say this? (Remember, the baron never lies.) Slide14: Musketeering swordplay. At the royal fencing competition in France, the first four places were taken by Athos, Porthos, Aramis, and D'Artagnan. The sum of the places taken by Athos, Porthos, and D'Artagnan was 6. The sum of the places taken by Porthos and Aramis was also 6. What was the place taken by each of the musketeers if Porthos ranked higher than Athos? Slide15: Be fruitful and multiply. One day all of Mrs. Brown's grandchildren came to visit her. There was a bowl of apples and pears on the kitchen table. Mrs. Brown gave each child the same number of pieces of fruit without keeping track of which kind. Bobby got 1/8 of all the apples and 1/10 of all the pears. How many grandchildren did Mrs. Brown have? Slide16: Returnable bottles. A government program allows people to collect empty milk bottles and exchange them for bottles full of milk. Four empty bottles may be exchanged for one full bottle. How many bottles of milk can a family drink if it has collected 24 empty bottles? Slide17: Bottles Solution It’s not hard to see that the family can drink 6 + 1 = 7 bottles of milk, and it will have three empty bottles left. Then the family can borrow one empty bottle, exchange the four empty bottles for one bottle of milk, drink it, and return the bottle it borrowed. Thus, the family can drink eight bottles of milk. Slide18: Valentines Cards Brrr! It's been so cold where we live in the Midwest that yesterday the schools were closed! Fortunately for their parents I was able to take care of my nephews, Barney and Danny, and their cousin, Gina. We had lots of fun doing puzzles, playing games, and reading books, but by early afternoon the boys were ready to watch a video and Gina wanted to make valentines. I set up a valentine making station on the kitchen table, complete with red and pink paper, doilies, stickers, markers, glue, glitter and other things I had been saving for just such an occasion. After the video was over, the boys wanted to see Gina’s valentine creations. "Not until you guess how many I made," said Gina, holding her cards behind her back. "It would be more fun if you gave us some clues, Gina," suggested Barney. "Then we wouldn’t have to guess. We could figure it out." Always up for a challenge, Gina left the room and soon returned, ready with her clues. "OK, now listen, Barney. If I give half my valentines to my best friends at school, and then I give half of what is left over to my friends in my apartment building, I will still have enough valentines left over to give you, Danny, Aunty and Uncle Bill a valentine." Slide19: Christmas Presents 3 children, Danny, Gina and Barney, helped wrap the Christmas presents. "We wrapped 30 presents altogether," Danny said. "Danny and I wrapped half the presents, Gina added. "Danny and I wrapped 4/5ths of the presents,” boasted Barney, “and Gina and I wrapped 7/10ths of the presents! " Can you get this challenge "wrapped up?" How many presents did each child wrap? Slide20: The Quilt How many squares did you say you had in this quilt, Gina?" asked Danny "Sixteen. I counted them all so I know, its sixteen," said Gina. "Well, I hate to be one to disagree, but I think you have more than sixteen squares on that quilt!" said Barney, winking, "And I'll bet Aunty will agree with me!“ What do you think? Are there more than 16 squares on Gina's doll quilt? If so, how many squares can you find? Slide21: The Parade “We saw 7 clowns in the parade. All were riding vehicles. Some clowns were riding bicycles and the rest were riding tricycles (3-wheeled bikes). “There were 17 wheels in all," How many bicycles were the clowns riding?" Slide22: New Shoes One day, two mothers and two daughters went shopping for shoes. Their shopping spree was successful — each bought a pair of shoes, and all together, they had three pairs. How is this possible? Slide23: Athletes in Place Five athletes were returning from a cross-country race. Athlete C placed third, and athlete E placed second. From the following information, can you tell how athletes A, B, and D placed in the race? Athlete A was not last. Athlete A came in after E. Athlete D was not first. Slide24: Dogs on Trial Someone's dog goes around the neighborhood every night getting into people's garbage pails and making a mess. Some of the neighborhood kids say they know what the guilty dog looks like, but the culprit strikes at night, so it's hard to see. Each of the four witnesses has one and only one detail right, and each detail is described correctly by only one witness. Dan says the dog is white, fluffy, wears a red collar, and has a long tail. Karen says the dog is black, has short hair, wears a red collar, and has a long tail. Max says the dog is brown, has long, silky hair, wears a blue collar, and has a long tail. Emma says the dog is spotted, fluffy, wears a red collar, and has a short tail. Can you correctly describe the guilty pooch? Dogs on Trial- Solution: Dogs on Trial- Solution The dog is white, has short hair, wears a blue collar, and has a short tail. To arrive at the answer, begin by making a chart like the following: Next, cross out the details in each column that are repeated. (only one detail is described correctly by each witness: the dog can't be fluffy, can't wear a red collar, and can't have a long tail.) Now you have all the information you need: The dog wears a blue collar and has a short tail. The dog must be white, because Dan is wrong about the hair, the collar, and the tail, and he has to be right about one detail. Karen, Max, and Emma are wrong about the dog's color; therefore the dog must have short hair, because Emma has to be right about one detail. Slide26: Mystery Twins Two babies born on the same day in the same year with the same mother and father are not twins. Can you explain how this can be? The Value of Months If March = 43 and May = 39, then by the same logic, what does July equal? Slide27: Puzzling Relations A man named George was hurrying to get ready for a dinner party when Dan rang his doorbell. "I'm just rushing off to a dinner party," said George, "but I'm sure it would be fine if you came along." So the two went off together. When they arrived at the party, George, who always enjoyed getting people to use their heads, introduced Dan to the other guests with the following rhyme: "Brothers and sisters have I none, But this man's father is my father's son." How were George and Dan related? Slide28: Which Way? Once a boy was walking down the road, and came to a place where the road divided in two, each separate road forking off in a different direction. A girl was standing at the fork in the road. The boy knew that one road led to Lieville, a town where everyone always lied, and the other led to Trueville, a town where everyone always told the truth. He also knew that the girl came from one of those towns, but he didn't know which one. Can you think of a question the boy could ask the girl to find out the way to Trueville? Slide29: Cups Up Take three paper cups and put them in a row. Turn the first and third cups upside down, but leave the middle cup right side up. Your task is to get all the cups right side up, but you must follow these rules: You have only three moves. For each move, you must turn over two cups at a time—never one at a time. Slide30: Exactly Two Draw a grid made up of six horizontal squares and six vertical squares. The grid will have 36 squares. Place 12 pennies on the grid, one to a square, so that each of the six horizontals, each of the six verticals, and each of the two diagonals contains exactly two pennies. Slide31: A Pocket Full of Coins Janice has €7.56 worth of coins in her pocket. The coins are of four different denominations, and she has the same number of each denomination. What are the four denominations, and how many of each does she have? Slide32: Average Speed Louise runs the first half of a race at 5 miles per hour. Then she picks up her pace and runs the last half of the race at 10 miles per hour. What is her average speed on the course? Wrap It Up You have 100 yards of ribbon on a spool, and you need 100 lengths of ribbon 1 yard long. It takes you 1 second to measure and cut each yard. How long will it take you to come up with the 100 pieces of ribbon? Slide33: Who Rocked the Boat? Three boats — one red, one blue, and one yellow — were out on the river this morning. By reading the following clues, can you tell the color and type of each boat, who is on each boat, and which country the people come from? Write your answers on a chart like this one: The woman is not in a yellow boat and is not from France. The red boat is not from Italy. The kids are in a blue boat, but they are not from Italy or Sweden. The man and his dog are on a yacht with an Italian flag. The sailboat is from France, while the canoe is red. Fill in the Missing Square : Fill in the Missing Square Can you fill in the missing square with the number that logically belongs there? Slide35: Where's the Fruit Juice? A catering company sells large containers of apple juice and large containers of orange juice. Right now the company has six containers, each holding the following amounts: Container A: 30 litres Container B: 32 litres Container C: 36 litres Container D: 38 litres Container E: 40 litres Container F: 62 litres Five of the containers hold apple juice, and one container holds orange juice. Two customers come into the shop. The first customer buys two containers of apple juice. The second customer buys twice as much apple juice as the first customer. Which container is holding the orange juice? Slide36: 5 Doggies The dog named Jam is heavier than the dog named Jelly. Copper weighs more than Brandy but less than Pumpkin. Brandy weighs more than Jelly. Pumpkin weighs less than Jam. List the dogs in the order of their weights, starting with the heaviest. Slide37: How Many Students? A new school has opened with fewer than 500 students. One-third of the students is a whole number. So are one-fourth, one-fifth, and one-seventh of the students. How many students go to this school? How Many Coins? A bag holds 50 coins that add up to $1.00. How many coins of each denomination (value) are in the bag? Slide38: Piano Lessons Abigail, Bettina, Cynthia, and Dahlia all began piano lessons last year. Cynthia took twice as many lessons as Bettina. Abigail took 4 lessons more than Dahlia but 3 fewer than Cynthia. Dahlia took 15 lessons altogether. How many lessons did Bettina take? Slide39: More Penny Candy Back in the days when candy cost just a few cents a piece, Alice was able to buy exactly 100 pieces of candy for a euro. Some of her candy cost 10 cents a piece; some of her candy cost 3 cents a piece; and some of her candy cost 1 cent for 2 pieces. How many pieces of each price candy did Alice buy? Slide40: On a distant island live three types of humans - Knights, Knaves and Normals. The Knights always tell the truth, the Knaves always lie, and the Normals sometimes lie and sometimes tell the truth. Detectives questioned three inhabitants of the island - Al, Bob, and Clark - as part of the investigation of a terrible crime. The investigators knew that one of the three committed the crime, but did not at first know which one. They also knew that the criminal was a Knight, and that the other two were not. How they knew these things is not important for the solution. Additionally, the investigators made a transcript of the statements made by each of the three men. What follows is that transcript: Al: I am innocent. Bob: That is true. Clark: Bob is not a Normal. After carefully and logically analyzing their information, the investigators positively identified the guilty man. Was it Al, Bob or Clark? Slide41: Chewing Gum Some problems have a solution that is easy to find, but the best solution is hard to find. The purpose for this homework is to look for the best solutions. There are 10 gumball machines. Most of the machines have gumballs that weigh 1 gram, but one of the machines has gumballs that weight 1.2 grams. You can't tell the difference between them just by holding them. You need to use a scale. You can take as many gumballs out of the machines as you need. How can you determine which machine has the heavier gumballs while using the scale as few times as possible? Slide42: Marbles 1 This time you have a balance instead of a scale. The way a balance works is that you place items in each side, and the balance will tilt toward whichever side is heavier. You have 8 marbles. Most of them have the same weight, but one marble is slightly heavier than the others. Again, you can't tell the difference just by holding them. There is a way you can tell which is the heavy marble while using the balance only twice. How? Slide43: Marbles 2 Now you have 12 marbles. Most of them have the same weight, but one marble is slightly different. You don't know if the different marble is heavier or lighter than the others. How can you tell which is the different marble while using the balance only three times?