Problem solving to start Middle or High School Math classes for the month of March 2013!

1. March Problem Solving
Modeling with
Mathematics (MP4)
adapted from MTMS Feb 2013 & Dec 2013

2. 3/1/13 What’s Your Favorite?
A company surveyed students about their
favorite flavors of ice cream. Of those
students surveyed, at least 1 was a girl
and more than 93% were boys. What is
the smallest possible number of students
in the survey?

3. 3/4/13 A Prime Example
What is the smallest three-digit prime
number whose digits are also prime?

4. 3/5/13 Pedal Faster!
In a 20-mile bicycle race, Matthew went
twice as fast as Tim, and Sally went
twice as fast as Matthew. Sally finished
3.75 hours ahead of Tim. What was
Matthew’s average speed (in miles per
hour) for the race?

5. 3/6/13 Make a Prediction!
If the letters in the following sequence are
repeated indefinitely, what is the 2000th letter
in this pattern?
HIGHSCHOOLMATHEMATICSHIGHSC

6. 3/7/13 Sweet Tooth
Mr. Zucker has a bag of candy containing less than
100 pieces, which he will distribute to the class. If he
makes groups with 2, 3, or 4 pieces of candy, he will
have 1 piece leftover in the bag. If he makes groups
with 5 pieces of candy, he will have no candy left in the
bag. How many pieces of candy could be in Mr.
Zucker’s bag? List all possibilities.

7. 3/8/13 Fun with Fractions
A unit fraction, such as 1/2, 1/11, and
1/25, is a fraction in the form of 1/n, where
n is a positive integer. Find a pair of unit
fractions such that their difference is 1/72.

8. 3/11/13 A Power-full Problem
Observe the following set that contains 26
powers of three:
30, 31, 32, 33, . . . , 325
How many numbers in the set will have a
units digit (ones digit) of 1?

9. 3/12/13 Get the Best Deal!
Bob’s Furniture is running a promotion. Any purchase
less than $4500 receives a 10% discount; a purchase
of $4500 or more receives a 20% discount. Katie has
determined that it is actually cheaper to buy more
merchandise and bring her bill up to $4500 to obtain
the 20% discount. Under what circumstances will this
be true?

10. 3/13/13 An Age-Old Problem
When asked his age, Ryan said,
“My age is a number between 30 and 60,
the difference between the digits is 4,
and the mean of the digits is 6.” How old
is Ryan?

11. 3/14/13 I Pledge to Solve This Problem
Shane is standing next to the school’s flagpole.
He notices that the flagpole’s shadow from the
sun extends across 3 full sections of sidewalk (all
the same size), and that his shadow only extends
across 3/4 section of a side-walk. If Shane is 6 ft.
2 in. tall, how tall is the flagpole?

12. 3/15/13 Turn up the Volume
A new website called MyTunes.com charges for
songs on the basis of the length of each song.
“Deriving Me Crazy” is 3 minutes, 36 seconds long
and costs $1.08. “Tessellate My Heart” is 2 minutes,
44 seconds long and costs $0.82. How much would
MyTunes.com charge for “Polygon Forever,” which
is 3 minutes, 12 seconds long?

13. 3/18/13 Mean, Median, Mode!
License plate numbers issued in Norfolk
County contain 6 digits, each in the range of
0–9. For the 6 digits of Deanna’s license plate,
the range is 9, the mean is 4.5, the median is
5.5, and the mode is 6. What are the 6 digits
on Deanna’s license plate?

14. 3/19/13 A Statistical Situation
A set of 5 different positive integers has a
mean of 33 and a median of 40. Within
this set, how large can the greatest
number be?

15. 3/20/13 1, 2, 3, 4, 5, 6, 7, 8, ..
To play the math game Bizz Buzz, you begin
counting at 1 but skip all multiples of 3 and 5
and all numbers that contain the digits 3 and 5.
In this game, the number 16 is the 8th number.
If you continue this game, what is the 25th
number?

16. 3/21/13 Lots of Options!
Students at a school picnic can choose either a
hamburger or a hot dog and can choose among
ketchup, mustard, and cheese for toppings. If
students can have all, some, or none of the
toppings, how many different sandwiches can be
made?

17. 3/22/13
If -11 is the output, what’s the input?
If -11 is the output, what’s the input?
In each pair of numbers below, the input is the first
number and the output is the second number. After
examining the five input and output pairs below,
determine the output if the input is –11.
(–1, 3) (0, 6) (2, 12) (10, 36) (97, 297)

18. 3/25/13 Which number doesn’t belong?
Of the following 10 numbers, one is unlike the
other 9 numbers. Which number does not belong
in this 10-number set? Hint: Consider
multiplication.
{6, 15, 39, 65, 77, 95, 105, 133, 221, 437}

19. 3/26/13 Rolling the Dice
Two dice are rolled. What is the
probability that the numbers on the dice
will be consecutive?

20. 3/27/13 Who Am I?
I am a number. I am the sum of the measures of
the interior angles of a triangle, divided by the
number of sides in a dodecagon, multiplied by the
most frequently occurring digit in the first 5
numbers in the sequence 1, 4, 16, . . . , and less
the median of those same 5 numbers. What
number am I?

21. 3/28/13 Minty Fresh
The Bits o’ Mints Company sells tins that contain
24 cylindrical mints that are 1 cm wide and 1/2 cm
tall. The mints are arranged 4 wide, 3 deep, and 2
high and fit snugly in their rectangular prism tin.
How many cubic centimeters of space in the tin
are empty?

22. 3/29/13 A Geometric Probability Problem
Joel’s living room wall is 13 feet long with 2-inch
wide vertical support beams every 16 inches,
starting at the right edge of the wall. If Joel wants
to hang a mirror that is right edge of the wall. If
Joel wants to hang a mirror that is secured to one
of the support beams, what are the chances that a
randomly placed nail will go through a beam?

23. Doing Good Deeds
Bobby was inspired to do good deeds in his
community. The first day, he did 1 good deed for 2
neighbors. When they asked how to repay him, he
told them to do 2 good deeds for 2 other people
the next day. each neighbor complied. Bobby
repeated what he did the first day. After how many
days would 1000 good deeds have been done?