Self-answering problems contain their
own answers. The winners from the September 2005 contest can be read
here. In case that isn't enough, here are
more questions submitted by our readers. The answers are highlighted in
green. They presented in the order received. If you
have your own questions to add, please e-mail them to
jquinn@awm-math.org.
- Express, in Roman numerals, the number before FIVE.
(Head-Royce School Math Club in Oakland, CA)
- Express, in binary, the number of different
ways one can answer a 100 question true/false test. You are not allowed to
look it up on Google! (Head-Royce
School Math Club in Oakland, CA)
- Determine lim
(n®∞)
(1+1/n)n? (Head-Royce
School Math Club in Oakland, CA)
- At time t=0, water begins pouring
into an empty sink so that the volume of water is changing at a rate V'(t)=cos
t. For time t=k, where 0< k < π/2, determine the amount
of water in the sink.
(Raymond Greenwell, Hofstra University)
- The cost of a widget varies according to
the formula C'(t)=-sin t. At time t=0, the cost
is $1. For arbitrary time t, determine a formula for the
cost. (Raymond Greenwell,
Hofstra University)
- What is the name of the
Washington Monument? (Monty
Korpe, Virginia Tech)
- What is the opposite of the second
derivative of f(x) = sin (x)?
(Rheta Rubenstein, University of Michigan-Dearborn)
- What is the fourth derivative of
f(x) = sin (x)?
(Rheta Rubenstein, University of Michigan-Dearborn)
- What is an equation for the tangent to the
identify function at y = 1?.
(Rheta Rubenstein, University of Michigan-Dearborn)
- Besides zero, how many other numbers are additive identities for the reals?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is the
one identity element for multiplication over the reals?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- How many factors does
2 have?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- How many letters are in the
number four?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is the reciprocal of the
reciprocal of 7?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- How many lines of symmetry are
there in a regular 4-gon?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- A fair spinner is
1/2 blue and 1/2 white. What is the
probability that a spin lands in the blue half?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What fraction of the letters in “a
third” are vowels? (Rheta
Rubenstein, University of Michigan-Dearborn)
- What fraction of the letters in “fifth”
are vowels? (Rheta Rubenstein,
University of Michigan-Dearborn)
- What function is the derivative
of the function f(x) = ex?
(Rheta Rubenstein, University
of Michigan-Dearborn)
- What is the slope of the line
y = 0?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is the perimeter of a unit
regular 4-gon?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- Describe the relationship among
the ls in “parallel.”
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What do you do to the length of
an edge of a square to find its area?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- How many digits in 4444 are
four?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- Share your
reflection about the relationship of a figure to itself if it has one
line of symmetry. (Rheta
Rubenstein, University of Michigan-Dearborn)
- What fraction of the letters in
“two-thirds” are in “thirds?”
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is one more than the
reciprocal of
F?
(Rheta Rubenstein, University
of Michigan-Dearborn)
- What is the square of the square
root of 23?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What statistical measure tells
you how far the values in a data set range?
(Rheta Rubenstein, University
of Michigan-Dearborn)
- A
quarter
is what fraction of a dollar? (Rheta
Rubenstein, University of Michigan-Dearborn)
- A
fifth
is what fraction of a gallon? (Rheta
Rubenstein, University of Michigan-Dearborn)
- What type of angle is made by the
first letter of ACUTE?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is the shape of the last
letter in arc?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is the
product when two numbers are multiplied?(Rheta
Rubenstein, University of Michigan-Dearborn)
- How would you describe the double
“r” in recurring?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What type of angle is made by the
last letter in “right?”
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What is the
standard way to pronounce “standard?”
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What do you call the base of the
first letter in the word “vertex?”
(Rheta Rubenstein, University of
Michigan-Dearborn)
- What part of a king’s body was
first used to define the measure known as a “foot?”
(Rheta Rubenstein, University
of Michigan-Dearborn)
- What is the output of the
identity function when the input is 36?
(Rheta Rubenstein, University of
Michigan-Dearborn)
- Some mathematical symbol produces
surprisingly large outputs for relatively small inputs!
What is it? (Rheta Rubenstein,
University of Michigan-Dearborn)
- How many times would you
expect to roll a fair die in order to obtain a "6"
for the first time? (Roger Nelsen, Lewis & Clark
College)
- Find the area of a square with perimeter equal to 16.
(Roger Nelsen, Lewis & Clark College)
- Find the volume of a cube whose surface area is 216.
(Roger Nelsen, Lewis & Clark College)
- Find the perimeter of an equilateral triangle whose area is equal to
12√
3. (Roger Nelsen, Lewis & Clark College)
-
(Roger
Nelsen, Lewis & Clark College)
- What is the only prime number divisible by
15,485,863? (Gregory
Hartman, Virginia Military Institute)
- Give 1 of the
2 roots of x^2 - 3x + 2. [Or Give 1 of the 2 roots of x^2 - 3x + 2.]
(Gregory Hartman, Virginia Military Institute)
- Give 1,
4 digit prime number that ends with
27. (Gregory Hartman,
Virginia Military Institute)
- Find the sum of the factorials of the
digits of 145. [145 (= 1!
+ 4! + 5!)] (Larry Lesser, University of Texas at El
Paso)
-
To the tenths place, find
the chi-square value that would indicate significant association at the .05
level from a 2x3 contingency table.
[6.0 (which equals 2 x 3)]
(Larry Lesser, University of Texas at El Paso)
-
State
one integer that is neither prime nor
composite. (Larry Lesser, University of Texas at El Paso)
-
Find the smallest natural
number no greater than one-thousand that
contains the letter a. (Larry Lesser, University of
Texas at El Paso)
-
In what kind of units
would you express the area of a “square”?
(Larry Lesser, University of Texas at El Paso)
-
Find all numbers whose
spelling has exactly four letters.
(Larry Lesser, University of Texas at El Paso)
-
What’s the approximate
probability of winning the lottery, if we treat it as a
zero-sum game? (Larry Lesser,
University of Texas at El Paso)
-
From the letter gamma, how
many letters do you have to count through the Greek alphabet to reach the
letter xi, giving the answer as a Roman
numeral. (Larry Lesser, University of Texas at El Paso)
-
Note
integer near
eight (Larry Lesser, University
of Texas at El Paso)
-
I’m a solution to x2
+ 1 = 0. What am i?
(Larry Lesser, University of Texas at El Paso)
-
How often are
hands shook, if five people all shake hands with everyone?
(Dave Ehren, Macalester College)
-
How many diagonals does a
five-sided convex polygon have?
(Dave Ehren, Macalester College)
-
From 185, subtract
thirty five times. What do you get?
(Dave Ehren, Macalester College)
-
What's
1! + 4! +
5!? (James Tanton, St. Mark's
Institute for Mathematics)
-
What's
4! + 0! +
5! + 8! +
5! ? (James Tanton, St.
Mark's Institute for Mathematics)
-
How many different types
of infinity did Cantor discover?
(James Tanton, St. Mark's Institute for Mathematics)
-
In a twelve-hour period,
how many times to the minute and the hour hands of a clock align?
(James Tanton, St. Mark's Institute for Mathematics)
-
One to any power equals
...? (James Tanton, St. Mark's Institute for
Mathematics)
-
Two lists:
One contains
three consecutive positive integers and the other
five consecutive positive
integers. Their union has six members and their symmetric difference
four.
The product of the numbers in first list equals the product of the numbers
in the second. What are the numbers appearing in the lists?
[4,5,6 and 1,2,3,4,5] (James
Tanton, St. Mark's Institute for Mathematics)
-
Sum of the cubes: Find
3^3 + 7^3 +
0^3. (Art Benjamin, Harvey Mudd
College)
-
What is the sum of the
proper positive factors of six? (or insert your
favorite
perfect number) (Robert Vallin, Slippery Rock University)
