 Round the World on a Wire  Terry Trotter
Algebra, difficulty level 2. A wire is wrapped around the equator of the earth. Then extra wire is spliced in. Can you walk under the slack that results?
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 Row, Row, Row Your Boat  Ethel Breuche
Algebra, difficulty level 2. Cassie and Mat are sinking fast on their raft. How fast must Cassie bail so that they don't have to swim to shore?
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 Sam and Teri Revisited  Terry Trotter
Algebra, difficulty level 3. A bank account depositwithdrawal problem with a difference.
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 Sam and Teri's Bank Accounts  Terry Trotter
Algebra, difficulty level 1. Sam and Teri have bank accounts. Sam always withdraws money; Teri always saves it. When will they have equal balances, or will they?
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 September Squares  Cynthia Lanius and Steve Risberg
Algebra, difficulty level 2. Use a variable to explain how you can be given the sum of four dates
that form a block on a calendar and determine what the four dates must be.
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 A Sequence of Numbers  Asher Walkover
Algebra, difficulty level 2. Find the second number in a Fibonaccilike series.
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 Sierpinski Stages  Steve Risberg
Algebra, difficulty level 2. Find and use patterns to determine the total perimeter of an interesting shape.
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 A Space Diagonal  Terry Trotter, MATHCOUNTS
Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes.
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 The Spider and the Fly  J. A. H. Hunter
Algebra, difficulty level 2. A spider presents a challenge to a fly: solve a math problem and escape!
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 The Spiral on the Can  Ethel Breuche
Algebra, difficulty level 3. By using the Pythagorean theorem, students can find the length of the spiral painted on a can.
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 Stina's Hike  Annie Fetter
PreAlgebra, difficulty level 2. Choose the graph that best represents Stina's hike.
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 The Straggler Shakes Hands  Melissa Kennedy, Susan Rose, Ethel Breuche
Algebra, difficulty level 3. There were one hundred fortyone handshakes in all. How many people did the straggler know? This puzzle involves a quadratic expression and triangular numbers.
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 Sums, Quotients, and Remainders  Terry Trotter
Algebra, difficulty level 3. Given the sum of two numbers and information about the quotient and
remainder when they are divided, find the larger number, then
solve the same sort of problem in a general case.
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 A Surprising Sequence  Steve Risberg
Algebra, difficulty level 2. In a Fibonacci sequence, the first number is 1 and the tenth number is
111. Find the second number.
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 Swapping Marbles  Lillian Ray, Steve Risberg, and Steve Weimar
Algebra, difficulty level 3. Three kids swap marbles in an interesting way. After the swapping, which of the three had gained the most marbles? How many did they gain?
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 Take Me Out to the Ballgame  Annie Fetter
Algebra, difficulty level 4. Determine how many innings a pitcher has thrown as his Earned Run Average changes during a game.
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 A Tale of Two Intercepts  Terry Trotter
Algebra, difficulty level 3. Find the distance between two yintercepts.
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 Tatianna and the Troll  Terry Trotter, revised
Elementary, difficulty level 3. Tatianna tests the troll... and neither loses nor gains.
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 TelePlus  Terry Trotter
Algebra, difficulty level 1. Find the cost of one phone that is part of a threeinone communications package deal.
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 Tennis Anyone?  Ethel Breuche
Algebra, difficulty level 1. Use algebra, inequalities, and ratios to find the greatest number of matches a player could have won before the weekend to achieve the win ratio of .503 after the weekend.
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 Texting 1, 2, 3  Steve Risberg
Algebra, difficulty level 2. Determine the pricing of Kheri's cell phone texting plan.
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 That's Interesting!  Steve Risberg
Algebra, difficulty level 3. Two men follow different strategies for saving money. Who winds up
with more?
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 The North Hunterdon Triangle  Annie Fetter
Geometry, difficulty level 2. Given points O:(0,0) and Q:(a,0), describe the possible locations of
point P such that triangle OPQ is first isosceles and then equilateral.
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 The Teddy Bears' Banquet *  Claire Mead
Math Fundamentals, difficulty level 3. How many bears can be seated at the banquet?
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 Three Consecutive Integers  Annie Fetter
Algebra, difficulty level 1. Use a variable to explain an interesting relationship that can be found between three consecutive integers.
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 The Three Jelly Bean Jars  Terry Trotter
Algebra, difficulty level 2. Three brothers buy jelly beans. The jelly beans are in jars that are three different sizes. How many jelly beans does each brother buy?
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 Tiffany's Triumphs  Terry Trotter
Algebra, difficulty level 1. Given the number of games that Tiffany has played so far and the number that she has won, how many games would she have to win in a row to get her winning percentage up to 60%?
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 Timber!!!  Lisa and Judy Gardner
Math Fundamentals, difficulty level 3. Determine the lengths of two pieces of a damaged redwood tree.
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 Time Trial Triumphs  Steve Risberg, Terry Trotter, and Annie Fetter
Algebra, difficulty level 2. At 9:05 a.m. Ernesto starts riding at a speed of 440 yards per
minute. At 9:20 a.m. Johnny starts riding, but he's going 20% faster
than his little brother. At what time, to the nearest minute, will
Johnny catch Ernesto?
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 To B or Not To B  Steve Risberg
Algebra, difficulty level 2. Given a letter pattern, find expressions for the number of B's and the
ratio of B's to total letters in the nth term.
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 To Grandmother's House We Go  Ethel Breuche
Algebra, difficulty level 4. Red Riding Hood goes to visit Grandmother for the holidays at the same time that Grandmother heads out to visit Red. What is the ratio of their speeds?
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 Touchdown Toddlers  Terry Trotter
Algebra, difficulty level 2. Two little boys run an unusual race on a professional football field, and everybody comes out a winner!
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 Triangle Possibilities  Steve Risberg
Algebra, difficulty level 2. Given information about side lengths of a triangle, determine possible dimensions.
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 Triangle Probability  Annie Fetter
Algebra, difficulty level 3. A point is randomly selected from within a triangle with vertices at (0,0), (0,4) and (6,0). What is the probability that the xcoordinate of the selected point is less than the ycoordinate?
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 A Triangle's Area  Canadian Open Math Challenge 1999 via Tim Lang
Algebra, difficulty level 3. Find the "b" values of two lines needed to form two congruent triangles of a given area.
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 Triangular Number Identities  Terry Trotter
Algebra, difficulty level 3. Prove two famous theorems of ancient number theory: the sum of any two consecutive triangular numbers is a square number, and the product of 8 and any triangular number, increased by 1, is a square number.
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 Tribonacci  Terry Trotter
Algebra, difficulty level 3. Find the second and third terms of a "Tribonacci" sequence.
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 TrickorTreat Box  Terry Trotter
Algebra, difficulty level 1. Harvey and his classmates make trickortreat boxes in math class and use a special formula to find the volumes.
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 Tunnel Time  Annie Fetter, Ian Underwood, Suzanne Alejandre
PreAlgebra, difficulty level 2. At what time does the end of the train emerge from the tunnel?
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 Two for Two  Annie Fetter
Algebra, difficulty level 3. Two numbers have a ratio of 5:3. The larger number is 36 more than half the difference of the two numbers. What are the two numbers?
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 Two for Two More  Annie Fetter
Algebra, difficulty level 3. Two numbers have a ratio of 4:3. The greater number is 60 more than 8 times their difference. What could the two numbers be?
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 The Unhappy Carpenter  Ethel Breuche
Algebra, difficulty level 1. A carpenter agrees to be paid a certain amount of money when she works, and to repay money on the days she doesn't work. Find the number of days she worked if she earned $77.00.
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 Up the Down Elevator  Ethel Breuche
Algebra, difficulty level 2. Juanita has to use a freight elevator to deliver packages but can use the passenger elevator to return. What is her average speed for the entire trip?
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 Valentine Candy  Ethel Breuche
Algebra, difficulty level 2. A vendor who sells Valentine candy boxes wants to raise the price. For every twentyfivecent increase he loses two customers. At what price should he sell the boxes to achieve the maximum profit?
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 Voter Turnout  Steve Risberg
Algebra, difficulty level 2. A group of students collected data on voter turnout for the recent
election and plotted graphs broken down by age groups. Can you match
each age group with its graph?
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 Walter's Weird Wages  Terry Trotter
Algebra, difficulty level 2. Walter's eccentric parents give their son his housework wages in a strange way. Can you determine how much he receives?
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 The Way the Crazy Crow Flies  Janet Bowers
Algebra, difficulty level 3. A crazy crow flies back and forth between two trains that are approaching each other on parallel tracks. How far does the crow fly?
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 The Weight of Bart's Brick  Terry Trotter
Algebra, difficulty level 1. Bart was asked by his construction foreman about the weight of a brick. Bart's answer befuddled his boss. (But not you.)
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 What's My Angle?  Terry Trotter
Algebra, difficulty level 3. Using concepts of vertical angles and supplementary angles, solve two quadratic expressions to find the measure of a given angle.
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 What's My Line?  Terry Trotter
Algebra, difficulty level 1. Given a set of eight points in the Cartesian plane, find the three that are collinear.
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