Figure This! Math Challenge
Week 43
Question: The American flag has 50 stars, one for each state. The rows are of two different lengths. Each row has one more star or one fewer star than the row next to it. Use these clues to figure out how the stars are arranged.
Hint: Select a number of stars for one row; then use the information given to test some possible patterns.
Week 42 Challenge Question
Question: In the history of college football’s Rose Bowl, no team’s final score has ever been 11 points. How many different ways are there for a team to score 11 points?
Hint: In American football, a team may score points in the following ways:
- 8 points (touchdown and 2-point conversion)
7 points (touchdown and 1-point conversion)
6 points (touchdown and no conversion)
3 points (field goal)
2 points (safety)
Week 41 Challenge Question
Question: Paper money, such as dollar bills, with serial numbers that read the same backwards as forwards are sometimes called "radar bills." How common are radar bills?
Hint: Serial numbers on US bills have eight digits. How many different serial numbers are possible?
Week 40 Challenge Question
Question: How would Tessellation hit a golf ball from the tee to make a hole-in-one?
Hint: The angle at which the ball bounces off the wall will have the same measure as the angle at which it hit
the wall.
the wall.
Week 39 Challenge Question
Question: Helix and Polygon both used the same number of identical concrete pieces to make their patios. The area of each patio is the same: 180 square meters. What are the dimensions of a single piece of concrete?
Hint: Notice how the pieces fit together on Polygon’s patio. What is different about the way the pieces fit on Helix’s patio?
Week 38 Challenge Question
Question: Monday’s child is fair of face; Tuesday’s child is full of grace. On what day of the week were you born? Can you devise a method to find the day of the week for any date?
Hint: January 1, 2000 was a Saturday; January 1, 1999 was a Friday. (But don’t forget leap years. The year 2000
is a leap year.) An algorithm is a step-by-step process for completing a task. Algorithms are used by those who follow routines or recipes in their work: computer scientists, factory workers, statisticians, and chefs, among others.
is a leap year.) An algorithm is a step-by-step process for completing a task. Algorithms are used by those who follow routines or recipes in their work: computer scientists, factory workers, statisticians, and chefs, among others.
Week 37 Challenge Question
Question: How many colors of states are on a map of the US? Mapmakers use different colors on states that share a border. What is the least number of colors needed to color a map of the states west of the Mississippi River in this way?
Hint: Try to fill in the map with as few colors as possible. Then try to show why using fewer colors would not work.
Week 36 Challenge Question
Question: What percentage does it take to win a vote? Twenty-two percent of the girls voted Yes; thirty percent of the boys voted Yes on the same motion. If everyone voted, did the motion pass?
Hint: Suppose 40 boys and 50 girls voted. How many of each voted Yes? Understanding percentages is necessary for people to make sense of information in the media, for businesses to summarize work data, for politicians to interpret the results of polls, and for manufacturers to make decisions about marketing.
Week 35 Challenge Question
Question: What shape is at the top of a fire hydrant? The water control valve on the cover of a fire hydrant has five sides of equal length and five angles of equal measure. Many common household wrenches will not turn these valves. Why not?
Hint: Think about an ordinary household wrench. Most wrenches have two parallel sides; that is, the sides are
everywhere the same distance apart.
everywhere the same distance apart.
Week 34 Challenge Question
Question: During the 100 meter dash in the 1988 Olympic Games in Seoul, Florence Griffith-Joyner was timed at 0.91 seconds for 10 meters. At that speed, could she pass a car traveling 15 miles per hour in a school zone?
Hint: How many meters in a mile? How many seconds in an hour?
Week 33 Challenge Question
Question: Some steps are 7 inches high and have a width of 10 inches. How far away should the ramp start to go up three steps?
Hint: Access ramps usually go up about 1 inch for every 12 inches. Slope is a measure of the steepness of an incline. Slope is used by civil engineers, builders, surveyors, and landscapers in constructing roads through
mountains, stairs in houses, and drainage ditches.
mountains, stairs in houses, and drainage ditches.
Week 32 Challenge Question
Question: Which wiper (see the figure below) cleans the greater area?
Hint: Draw models of the areas covered by each wiper, then cut them out and compare.
Week 31 Challenge Question
Question: In March, the National Collegiate Athletic Association (NCAA) holds a basketball tournament. As soon as a team loses one game, it is out of the tournament. The last unbeaten team is the winner. There were 64 teams in the 1999 men's tournament. In 1985, there were only 32 teams. How many more games were played in the 1999 tournament than in 1985?
Hint: When the final winner is determined, how many teams will have lost?
Week 30 Challenge Question
Question: The costs of combinations of frowns, smiles, and neutral faces are shown. How much is a smile worth?
Hint: Find a way to combine two of the rows or columns that have something in common.
Week 29 Challenge Question
Question: A newspaper headline reads: "Women’s salaries catching up to men’s." Using the information in the figure below from the U. S. census, do you think this is true?
Hint: Think of ways to describe and compare the growth in salaries.
Week 28 Challenge Question
Question: How many people would have to be in a school before it contained at least two people with the same first and last initials?
Hint: Consider a simpler problem. How many people would have to enter a room before it contained at least two people with the same first initial?
Week 27 Challenge Question
Question: Using the chart shown in the figure, estimate the biggest difference between the life expectancy of men and women in any year from 1920 to 1996.
Hint: A woman born in 1920 had a life expectancy of about 55 years at birth.
Week 26 Challenge Question
Question: Two players each roll an ordinary six-sided die. Of the two numbers showing, the smaller is subtracted from the larger. If the difference is 0, 1, or 2, player A gets 1 point. If the difference is 3, 4, or 5, Player B gets 1 point. The game ends after 12 rounds. The player with the most points wins the game. Is this game fair?
Hint: In a fair game, all players are equally likely to win. Play this game several times and record the results of each roll.
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