=EQUALS=
A CLUB OF INVESTIGATION AND DISCOVERY
January 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
Questions have points from 1 (easiest) to 10 (hardest). The average daily question will be 5 points. There will be approximately 150 points available each month.
All of these are doable by most any student, with minimal math knowledge or background, believe it or not! The hardest part of most is getting going. That's my fundamental lesson: how to get started.
I will try to have a spreadsheet accompanying each problem. These help me "Get a feel for the problem", plus a lot more! Answers will be posted - and methods - after a number of questions are on the board.
The majority of these questions I still answer the same way I answer these simpler questions ... The Challenge is still there - and I issue it here!
TEACHERS. PARENTS. STUDENTS.
Even now, I solve most of these problems with one simple algorithm. One.
Interested?
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THE CASE OF THE MYSTERIOUS "S"
7 Points
January 2, 2012
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How many points of intersection are there in the following design?
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6 Points
January 3, 2012
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“At the time of the Articles of Confederation, the major controversy related to land measurement and pricing. Early methods for allocating unsettled land outside the original 13 colonies were arbitrary and chaotic. Boundaries were established by stepping off plots from geographical landmarks. As a result, overlapping claims and border disputes were common. The Land Ordinance of 1785 finally implemented a standardized system of Federal land surveys that eased boundary conflicts. Using astronomical starting points, territory was divided into a 6-mile square called a township prior to settlement. The township was divided into 36 sections, each section measuring 1 square mile or 640 acres each.” (National Archives)
If 640 acres is the same as one square mile, then how far is the length of one acre (assuming here, the acre is a square)?
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THE CASE OF THE IRREGULAR FIGURE
6 Points
January 4, 2012
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What is the sum of the internal angles of this irregular polygon?
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THE CASE OF THE COMPOUNDING INTEREST
10 Points
January 5, 2012
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I borrowed $1,000 from the bank at the beginning of the year. To repay the loan, I'm making twelve payments (P) at the end of each month in 2012, at a monthly rate of 1%. What is my monthly payment?
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THE CASE OF THE MULTI-ROUTE TRIP
7 Points
January 6, 2012
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If I start at "Start", and if only moving down and hitting only one point at each level, then how many ways can I finish at "Finish"?
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THE CASE OF THE EXTENDED PIE SLICE
=8 Points
January 7, 2012
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If my slice of pie below is 20% of the whole pie, then what is the degree measure of angle α?
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THE CASE OF THE SYMMETRIC QUESTION
=8 Points
January 8, 2012
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Filling these six cells and assuming symmetry, the following grid can be fully populated:
If I had a 19 x 19 grid, then how many different symmetric designs could I create? Here are six examples:
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THE CASE OF THE THERMAL EQUALITY
7 Points
January 9, 2012
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The Celsius and Fahrenheit scales, named after these two gentlemen:
As you can see, the boiling point of water is 212°F (or 100°C). The freezing point of water is 32°F (or 0°C).
Are the Fahrenheit and Celsius temperatures ever the same?
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THE CASE OF THE TRIANGULAR CONUNDRUM
10 Points
January 11, 2012
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Suppose I have an equilateral triangle, and, bisecting each segment, create a smaller triangle:
"What's the size of the inside triangle relative to the starting triangle"? One-fourth. Instead of going 1/2 the distance on each segment, what if you go 3/4 the distance?
What's the size of the inside triangle relative to the starting triangle?
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THE CASE OF THE MESSY COUNTERTOP
5 Points
January 12, 2012
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My cube with 2" sides weighs 4 pounds. I drop it is a bucket filled to the top with water. My cube sinks.
What's the weight of the water spilling onto my countertop? |
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3 Points
January 13, 2012
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Each base in baseball is 90' apart. The pitching mound is 60'6" from home. That's an odd number.
If the pitching mound was at the intersection of the lines between home & 2nd, and 1st & 3rd, then how far would the pitching mound be from home?
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7 Points
January 14, 2012
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THE CASE OF THE STRAIGHT CIRCLE
6 Points
January 15, 2012
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Each equally spaced point on this circle is connected to every other point with a straight line. How many total lines are there?
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THE CASE OF THE TEETERING TOTTER
6 Points
January 16, 2012
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Each ball on these two balanced teeter totters weighs one pound:
TETTER TOTTER 1
TETTER TOTTER 2
TETTER TOTTER 3 Tetter Totter 3 is unbalanced. If I only have a 5 pound weight, then where would I place it below to balance my unbalanced teeter totter?
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10 Points
January 17, 2012
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If "n choose k" is defined as:
then what is the maximum value of:
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9 Points
January 18, 2012
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The cylinder on the right is one foot in diameter, the cylinder on the left four feet in diameter. I apply a downward force on the left cylinder, forcing the piston down.
If I have moved the piston on the left a foot, then how much have I raised the car on the right?
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8 Points
January 19, 2012
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In Rise of the Planet of the Apes, the following "Lucas Tower" (or Tower of Hanoi) was used to measure ape intelligence:
The goal of the game is to get all pieces to the next peg. The catch: you can only move one disc at a time, and you can never have a bigger peg on top of a smaller peg.
What is the minimum number of moves it will take in the above 8-disc game to complete the game?
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THE CASE OF THE RELATIVE CIRCLES
7 Points
January 20, 2012
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Jefferson High has 1000 students, and is at 6th and Grand. Washington High has 2000 students and is at 12th and Baltimore. I want to plot these two school, using latitude and longitude. Easy enough. But I also want to show their relative size. That is, I want the areas of the points (circles) to reflect the size of the population. Therefore, the area of Washington's plotted circle must be twice as big as Jefferson's plotted circle. If my point (circle) for Jefferson is 3 mm across, then how wide should my point (circle) for Washington be?
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THE CASE OF THE COUNTER-CLOCKWISE MOTION
8 Points
January 21, 2012
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The large gear on the right has a 9" radius, and spins at 1 revolution / minute. If the gear on the left has a radius of 3", then what is its rotational speed?
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THE CASE OF THE TRIANGULAR ENIGMA
8 Points
January 22, 2012
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To go from the top row in the pyramid below, the following rule applies:
How many black circles are there in the first 132 rows?
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THE CASE OF THE "i" IN THE SKY
6 Points
January 23, 2012
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THE CASE OF CIRCUMFERENCE INFERENCE
10 Points
January 24, 2012
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The great Eratosthenes was the first to estimate the circumference of the earth. While at City A (Aswan, now), he knew the sun would be directly overhead. (How? Sunlight shone straight down into a well). Let's assume Alexandria is 1600 miles away, and there's also a well there. The sun can't shine straight down that well, because it's overhead in Aswan. He placed a pole in the well, and had it stick 50' above the earth, perpendicular to the earth. It then blocked sunlight trying to reach the earth, thus casting a shadow of 22'. There. That's enough to estimate the circumference of the earth! (I've extended a couple of the rays below, for assistance. Also, the drawing is obviously not to scale).
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5 Points
January 25, 2012
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Mike's Doughnuts lost $100,000 in 2010, but earned a profit of $100,000 in 2011. What was the % change in the bottom line? |
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THE CASE OF THE QUESTIONABLE ORBITAL
9 Points
January 26, 2012
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The electron-shell diagrams for Oxygen and Uranium are below:
The inner shell can only hold two electrons, the next shell can hold, at most, eight electrons, the third shell 18 electrons, etc. The table for the shells and maximum electrons is below:
If the inner shell could only hold one electron, the second shell two electrons, the third shell three electrons, the fourth shell four electrons, etc., then what's the atomic number of our make-believe element that has the first 20 shells completely filled?
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THE CASE OF THE FLOWING CURRENT
8 Points
January 27, 2012
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The current of a river is 6 miles per hour. It takes a boat a total of 3 hours to travel 12 miles upstream and return 12 miles downstream. What is the speed of the boat in still water?
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6 Points
January 28, 2012
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The speed of light … nothing compares, The antiquated text book does declare! Instead I convert, and remove it from sight; To equal _________ furlongs / fortnight.
(For this calculation, assume the English conversion of Fortnight to days).
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THE CASE OF THE PYTHAGOREAN REVENGE
10 Points
January 29, 2012
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Find x.
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THE CASE OF THE DISAPPEARING SIGNAL
6 Points
January 30, 2012
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The brightness of a flashlight - or a headlight beam - is strong right in front of the source, but weakens over distance as the "signal" spreads out.
If the signal strength is only 1/4 as strong at one foot, and only 1/9 as strong after two feet, then strong is the signal strength at 4.5 feet?
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THE CASE OF THE ENCODED COLOR SPECTRUM
10 Points
January 31, 2012
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Every color in a spreadsheet is a mixture of red, green, and blue. As there are 256 shades of each color, there are 256^3 = 16,777,216 possible colors. To decode a large number into the red, green, and blue shades, we can consider "base 256", just as we would "base 10". If this algorithm works for 432 base 10:
then what is 9,742,585 base 256 (which gives the RGB shading)?
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