ONGOING+LIST+OF+IN-CLASS+PROBLEMS

These include selected situations motivated, explored, or mentioned in class.

//__**Cider Problem **__//  A bottle of cider costs 86 cents. The cider costs 60 cents more than the bottle.  How much does the just the bottle cost?

//**__Krazy Kids__ **//  [Version A] You knew that Mr. Jones has 2 kids, but that’s all you knew.  Then one day, you see Mr. Jones, and with him is his son. What  are the chances that Mr. Jones’ other kid is a girl?

[Version B] You knew that Mr. Jones has 2 kids, but that’s all you knew.  Then one day, you see Mr. Jones, and with him is his son. Mr.  Jones introduces his son, saying “This is my eldest, Jimmy.” What  are the chances that Mr. Jones’ other kid is a girl?

 My question: Are Versions A and B the same or different?

//__**Chain Links **__//  Given 4 pieces of chain consisting of 3 links each, explain how  all 12 links can be joined into a single circular chain by cutting  and rejoining only 3 links.

//__**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">GeoSquares **__// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Just by connecting rubberbands to pins,how many non-congruent squares <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> can be found in a 25-pin geoboard (that’s a 5 pin x 5 pin square board) ? How <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> about for an //n//2-pin geoboard ?

__//**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Ten-by-Ten Grid **//__ <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> How many squares are there in the 10 x 10 grid? <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> PS: I’d be more curious about an n x n grid

//**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">__Folding Paper__ **// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Show how to measure exactly 3 inches using only a sheet of paper that measures <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">8.5 inches by 11 inches.

//__**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Handshake Problem **__// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">There are 20 people in the room. Each person shakes hands exactly once with <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> everyone else. How many handshakes take place?

//__**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Always Tell The Truth **__// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> Bill could never tell the truth. Tom could never tell a lie. One of them said: <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> “The other one said he is Bill!” Which one said that?

//__**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Jackball **__// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> In one jackball team, jackers always lie, and non-jackers always tell the <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> truth. A new manager meets three players from the team, and asks the <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> first one if she is a jacker. The first player answers the manager. The <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> second player then says that the first player denied being a jacker. Then <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> the third player says that the first player is really a jacker. How many of <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> these three players are jackers?

//__**<span style="font-family: Arial,sans-serif; font-size: 14.6667px;">Condo Conundrum **__// <span style="font-family: Arial,sans-serif; font-size: 14.6667px;">In a certain Condo Complex, 2/3 of the men. Are married to 3/5 of the Women. <span style="font-family: Arial,sans-serif; font-size: 14.6667px;">What fraction of the people in the Condo Complex are married?

//**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">__Tibbs & Gibbs & Pibbs__ **// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> [1] We are given 37 tibbs. All 14 gibbs and all 21 pibbs are tibbs. If exactly 5 tibbs <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> are gibbs and pibbs, then how many tibbs are neither pibbs nor gibbs?

<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> [2] We are given 87 tibbs. All 34 gibbs and all 49 pibbs are tibbs. If exactly 9 tibbs <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> are gibbs and pibbs, then how many tibbs are neither pibbs nor gibbs?

//__**<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Dot Patterns **__// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> **>** Another One that’s neither Arithmetic nor Geometric (We saw three ways) ........ <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] [o] ........ <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] ........ <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] ........ <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] ... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] [o]
 * <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> > **<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> Marci’s Dots (Note connection to Triangular #s)

<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> **>** One that’s Arithmetic (We saw at least three ways) ...... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] [o] ...... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] .......... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] ...... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] .......... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] ...... <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">[o] [o] [o] [o]

//__ RBG Boxes __//
<span style="font-family: Arial,Helvetica,sans-serif; font-size: 14.6667px; line-height: 1.5;">You have three boxes: a red box, a blue box, and a green box. Inside each box is <span style="font-family: Arial,sans-serif; font-size: 14.6667px;">a single ball of the same colour as the box. Someone takes each ball out and <span style="font-family: Arial,sans-serif; font-size: 14.6667px;">puts it in a different box. You open the red box and discover a green ball. Is this <span style="font-family: Arial,sans-serif; font-size: 14.6667px;">enough information to tell what color ball is in the blue box? (If so, tell me the <span style="font-family: Arial,sans-serif; font-size: 14.6667px;">color; if not, explain or show why not).

//__ Hot Cocoa __//
<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">Patrick loves the taste of coffee in his hot cocoa. He drinks half <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">his cup of hot cocoa, then fills the cup with coffee. After stirring <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">and drinking another half-cup of the mixture, he again fills the <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">cup with coffee. He continues in this way until he has consumed <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">three cups of liquid. How much of the original hot cocoa remains <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;">in the cup?

//__ Final Digits Fun __//
<span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> What are the final two digits of 7^1997 ?

**//__A-B Cards__//**
There are 3 Cards, marked (Front/Back) as follows: A/A, B/B , A/B They are thoroughly shuffled, flipped, mixed, etc.

[Version 1]
> Draw a Card. You lay it on the table with your hand covering it completely. > What's the chance that the letter facing UP is different from the letter facing DOWN?

[Version 2] > Draw a Card. You lay it on the table with your hand covering it completely. > You peek at the letter facing UP, and it turns out it is an "A" > Now that you KNOW an "A" is facing UP, what's the chance that the letter facing DOWN is a "B" ?

My Question: Are Version 1 and Version 2 the same or different?

take Jenny to fill 1 swimming pool if she uses both pumps at the same time?
//__ **Mrs. Hoffman's Class** __// <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> Two-thirds of Mrs. Hoffman’s fifth-grade students are boys. To make the number <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> of boys and girls equal, 4 boys go to the other fifth-grade class, and 4 girls come <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> from that class into Mrs. Hoffman’s class. Now one-half of her students are boys. <span style="font-family: 'Arial','sans-serif'; font-size: 14.6667px;"> How many students are in Mrs. Hoffman’s class?

//__**Picnic with Friends**__// Tami, John, Fred, and Abdul are friends whose occupations are (in no particular order) nurse, secretary, teacher, and pilot. They attended a picnic and each one brought his or her favorite vegetable to share (tomato, carrot, asparagus, and green pepper, in no particular order). From the clues below, fit each friend’s name with their occupation, and favorite vegetable.

a) Tami is neither the nurse nor the teacher b) Fred and the pilot play chess together. The tomato lover and the teacher hate chess. c) Tami brought a green pepper. d) Abdul sat next to the tomato fan, and across from the asparagus lover. e) The secretary hates chess.

//__**Piles of Dimes**__// Julie has 25 dimes. She likes to put them in three piles with an odd number of dimes in each pile. In how many ways could she do this?

//__**Farmer Math**__// A farmer, when asked what number of animals she had, replied: “They are all horses but two, all sheep but two, and all pigs but two.” How many animals had she?

//__**Average Speed**__// I drove for One hour at 60 mph and then returned along the same route at 40 mph. What was my average speed for the entire round-trip?

__//**Mom’s Money**//__ Mom gives two-fifths of the money in her pocket to Dad, and then gives one-half of what’s left to Sister, and then gives two-thirds of what’s left to Brother. Then Mom splits what’s left with you. If you get 2.50 $, how much did Mom start with?

//__**Selling Apples**__// Each day, two women each have 30 apples to sell. On Monday, one woman sold her apples at 2 for a nickel; the other, at 3 for a nickel. They ended the day with 75 cents and 50 cents, respectively, or $1.25 in all. On Tuesday, they decided to pool their apples and sell them at 5 for a dime (they figured that this was the same as yesterday: 2 for a nickel and 3 for a nickel). At the day’s end, after selling all 60 apples at 5 for a dime, they had only $1.20. A dispute arose over the missing nickel. What happened to it?

//__**Diagonal Dilemma**__// Consider a //m// x //n// rectangle consisting of (//mn//) unit squares. How many unit squares will the main diagonal cross?