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Maths Matters

ABC is right-angled at A.  D is a point on AB such that CD = 1.  AE is the altitude from A to BC.  If BD = BE = 1, what is the length of AD?

Enter the letters A, B, C, D, E once in each row and column (in the first picture just A, B, C, D). The clues outside the grid indicate which letter appears first from that direction. In the third puzzle, for example, D must be the leftmost letter in both the first and third rows, and C must be the bottommost letter in the first and second columns.

This is another example of Einstein's riddles. It is said that this quiz was made up by the famous physicist and according to him 98% will not solve it.
There is a row of five different colour houses. Each house is occupied by a man of different nationality. Each man has a different pet, prefers a different drink, and smokes different brand of cigarettes.

Who has fish at home? Are you one of the 2%?

  1. The Brit lives in the Red house.

  2. The Swede keeps dogs as pets.

  3. The Dane drinks tea.

  4. The Green house is next to the White house, on the left.

  5. The owner of the Green house drinks coffee.

  6. The person who smokes Pall Mall rears birds.

  7. The owner of the Yellow house smokes Dunhill.

  8. The man living in the centre house drinks milk.

  9. The Norwegian lives in the first house.

  10. The man who smokes Blends lives next to the one who keeps cats.

  11. The man who keeps horses lives next to the man who smokes Dunhill.

  12. The man who smokes Blue Master drinks beer.

  13. The German smokes Prince.

  14. The Norwegian lives next to the Blue house.

  15. The man who smokes Blends has a neighbour who drinks water.

All of Pauline's favourite male relatives live in Europe. They are her father, her uncle, her first cousin, her brother, and her husband. In no particular order, their names are Daniel, Edgar, Wilfred, Luther, and Walter. Although they all live in Europe, no two men live in the same city. The cities in which they live are London, Paris, Rome, Madrid, and Berlin. From the clues given, try to determine not only the city in which each man lives and his relationship to Pauline, but his occupation as well, be it diplomat, correspondent, student, artist or professor. Assume her husband is only related to the other men through marriage to her.

1. The man in Berlin is the father of the correspondent and the diplomat is the father of the man in Paris.
2. Luther is the son of the man in Rome and Walter is the artist's son.
3. Daniel is the father of the man in Madrid and Wilfred is the father of the student.
4. Her cousin does not live in Paris

Three missionaries and three cannibals want to get to the other side of a river. There is a small boat, which can fit only two. To prevent a tragedy, there can never be more cannibals than missionaries together.
Ten students in Ms. Borowski's 6th grade class have been given a HUGE project!!! They have to research famous historical leaders (assigned--they can't even choose), and present them in front of the class using creative methods. However, they can at least work in pairs! Can you figure out which pairs presented whom, what presentation method they used, and what grade they received?

Tony and Lizzy received the same grade - one did a documentary and the other created a PowerPoint Presentation.

Tony lent Roxanne a book on Simon Bolivar for her project, not knowing that Jenna had already borrowed the same book from the library.

Sarah couldn't get Karl to do anything more than a timeline, which received the lowest grade.

Churchill ended up on a poster.

Zoe did not receive a B.

Danielle had already done numerous reports on Hitler, so she was thankful when she was assigned Churchill.

Although he wasn't supposed to, Joey helped Adam with his documentary of Hitler, since Joey was doing a report on the American leader during that time period

Creative Arts:
Five budding artists are meeting for lunch today at the new Thai restaurant in town. Use the following clues to determine the first (Allie, Billie, Callie, Donnie and Effie) and last (Adams, Booker, Cheek, Devlin and Efferman) names of each artist, along with her favorite medium (Acrylic, Oil, Pastels, Pen and Ink and Watercolor) current focus (Children, Dancers, Fish, Landscapes and Nests) of each artist, along with their "day job" (Banquet Server, Bartender, Cashier, Driver and Teacher.) Nobody shares the same name, favorite medium, current focus or day job with anyone else in the group.

1. The driver has never been drawn to landscapes and the teacher paints with either acrylic or oils. Ms. Efferman is currently focusing on either children or fish. The oil painter is either the bartender or the driver.

2. Billy paints with either acrylic or watercolors. The surname of the driver is either Cheek or Adams. Callie is either Ms. Adams or Ms. Devlin. Donnie uses either acrylic or oil paint. The oil painter is focused on either dancers or landscapes.

3. The watercolorist is either the banquet server or the teacher. The one working with pen and ink is neither Allie nor Effie. The acrylic painter is not focusing on landscapes or dancers. Neither acrylic nor watercolor is used to portray children.

4. Ms. Adams is either the bartender or cashier. Allie either uses pen and ink or is focusing on children. Either Allie or Billy is the banquet server. Ms. Adams' work portrays either dancers or fish.

6. Effie and the acrylic painter shared a pizza, Ms. Cheek had a salad, while the banquet server and the nest aficionado both had the soup of the day.

Three boxes are all labelled incorrectly, and you must get the labels right. The labels on the boxes read as follows:

To gain the information you need to move the labels to the correct boxes, you may remove a single item from one of the boxes. You may not look into the boxes, nor pick them up and shake them, etc.

Can this be done? If so, how? If not, why not?

What a week! Mr. Gilles, in charge of the Lost and Found, has been busy with students looking for lost items! Five students came, one on each day of the week, to retrieve their misplaced articles and possessions. So many came that Mr. Gilles has messed up his daily log! Can you help him piece the information back together?

1. The five students are Dominique, Mr. Harris, the one who lost a notebook, the one who retrieved her lost item Tuesday, and the one who came at noon.

2. Elsie picked her key up before Peterson came.

3. Ms. Sanson came at 9:50 a.m. to pick up a purse.

4. Birch came on Friday to pick up a lost item; Mary came on Wednesday.

5. Jacob spent an entire weekend worrying about his sweatshirt; he picked it up first thing on Monday.

6. Allen came earlier in the day than the one who picked up an iPod.

Girls: Mary, Dominique, and Elsie
Boys: Jacob and Allen