1. Huckleberry Toothpaste problem
Leo loves toothpaste. In fact he always has ten different flavors
lined up on a special toothpaste shelf in his bathroom. Leo wouldn't
think of brushing his teeth with just one layer of toothpaste on his toothbrush.
He always squeezes a double layer. He never uses two layers of the
same flavor of toothpaste. Leo's toothpastes are: Apple; Blackberry;
Cherry; Dandelion; Elderberry; Fruitti-Tutti: Grape; Huckleberry; Irish
Mint; and Juneberry. How many different double layers can Leo make
form his ten flavors of toothpaste if order doesn't matter?
2. Getting Dressed in the Dark
You awake early one morning and have to get dressed in the dark you
grab 3 items from a basket. What are the chances that you grab the jeans
and the sweatshirt from a basket that contains a pair of jeans, a pair
of khakis, a pair of sweat pants, a sweater, a t-shirt, a sweatshirt, and
3 pairs of socks: one red, one blue, and one green?
3. Fruit Juggler problem
A man is juggling 3 apples, 4 oranges, and 7 grapefruit. He drops
8 pieces of fruit. What is the probability that he drops all 7 grapefruit?
4. Compound interest problem
A $1000 deposit is made at a bank that pays 12% compounded annually.
How much will you have in your account at the end of 10 years?
5. Biology problem
If you start a biology experiment with 5,000,000 cells and 45% of the
cells are dying every minute, how long will it take to have less than 1,000
cells?
6. Pizza sharing problem
You and your friend have decided to order pizza and split it in half
to share. Right after the pizza was delivered, another friend stopped
by. You offered to give her half of your half of the pizza.
You had just finished shaking the parmesan cheese on your pizza when another
friend stopped by. Again, being the gracious friend you are, you
offered him half of your piece of pizza. Unfortunately, 3 more friends
came over and you gave each of them half of your piece of the pizza.
How much of the whole pizza did you give away to your friends?
7. Frustration problem
You were trying to solve a really hard math problem on a piece of paper.
You didn't like how you started out so you ripped the paper in half and
threw half away and kept half to continue writing on. You messed
up again so you ripped your remaining piece of paper in half and threw
half away. This process continued 6 more times. How much of
the original sheet of paper did you throw away?
8. Ticket sales problem
Mrs. White's drama class will be performing a musical in the spring.
They plan to sell advance tickets. Mrs. White wants to be sure they don't
sell more tickets than the auditorium will hold. She knows the seats are
arranged in a v-shape with one in the first row, three in the second row,
five in the third row and so on. She counts thirty-six rows in all.
How many tickets can the drama class sell? Can you find a rule to describe
"n" number of rows, using this type of pattern?
9. Band Halftime Show problem
Mr. Holland wants to have a great field show this year. So, he decided
to make a flat pyramid on the football field with the members of the marching
band. He wanted to make rows starting with one person at the front then
three people behind, then five people behind and so on. If there are 9
rows in the pyramid, how many students are there in band?
10. Paper Tearing problem
Take a sheet of paper and tear it in half. Place the two pieces
of paper atop one another, and tear them in half. Continue this process
through 20 such tears. How many sheets are now in the pile of paper?
If each sheet is .001 inches thick, how high is the pile of paper?
11. Dough problem
A baker has perfected magic bread dough that, when placed in the oven,
doubles in size every minute. He has further determined a special
measure of this dough that will exactly fill the oven in 30 minutes.
If the baker puts two special measures in the oven, when will the oven
be full?
12. Odd numbers
What is the sum of the 23rd, 33rd, 43rd odd numbers?
13. More Odd numbers
Beginning with the 50th odd number, find the sum of the following 50
odd numbers. (can you do it more than one way?!)
14. Logic Practice
Fill in the blank with "if," "implies," or "if and only if."
1. It is raining outside _______ the sidewalks are wet.
2. The ABCD is a parallelogram _______ ABCD is a rectangle.
3. The diagonals bisect each other _______ ABCD is a rectangle.
4. The three sides of the triangle, a, ,b, and c, are such that a^2
+ b^2 = c^2 _______ ABC is a right triangle.
5. ABCD is a rhombus and a rectangle _______ ABCD is a square.
6. ABCD is a parallelogram _______ a pair of opposite angles are congruent.
8. State the negation of:
If your credit rating is good and you fill out the application
form, then you receive a credit card.
15. Beetle Problem
As a biology project, Nicole is investigating how fast a particular
beetle population will grow under controlled conditions. She started
her experiment with 5 beetles. The next month she counted 15 beetles.
If the beetle population is growing exponentially, how many beetles
can Nicole expect to find after 2, 3, and 4 months?
16. Allowance Problem
A father complained that his daughter's allowance of $10 per week was
too much. The daughter replied, "Okay, Dad, how about this?
Will you give me a penny on the first day of the month, two pennies on
the second day of the month, four pennies on the third day of the month,
eight pennies on the fourth day of month, sixteen pennies on the fifth
day of the month, and so on for every day of the month?"
The father quickly calculated that he would
pay his daughter only $1.27 the first week, instead of $10, and he readily
agreed. Who was the foolish one, the father or the daughter?
17. Theater Seats problem
The Mathematics Theater has 25 seats in the first row, 27 seats in
the second row, 29 seats in the fhird row, and so on. How many seats
are in the 34-row theater?
18. Direct Reasoning Problems
For each of the following, state any (and all) conclusion(s) that can
be made. If no conclusion can be drawn, state "No conclusion possible"
and explain why there is no conclusion possible.
a. If a tenant at the Campus Students for Christ house breaks
his contract before June 15th, he will pay a $100 breakage fee.
Chris breaks his contract before June 15th.
b. If a tenant at Campus Students for Christ is caught with alcohol
or drugs in the building, he will receive a warning.
If a tenant receives a warning, he is put
on probation.
Chris is on probation.
c. If Bill lives at the Campus Students for Christ house, he must
attend Bible Study.
Bill does not attend Bible Study.
d. If Jane lives at the Campus Students for Christ house, she
can't have a pet.
Jane doesn't live at the Campus Students for
Christ house.
19. Drug Concentration Problem
A patient took a drug. At noon a blood sample was taken that
contained 50 mg of the drug. At 1:00, another blood sample was taken
containing 45 mg of the drug. This was done again at 2, 3, and 4
o'clock. The amounts were 40.5 mg, 36.45 mg, and 32.805 mg, respectively.
No more blood samples can be taken.
a) How much can you expect at 5 o'clock?
b) How much can you expect at 8 o'clock?
c) When will the amount of the drug drop below 10 mg (the safe limit)?
20. Furby Problem
The Wizard Toy Company is busy creating new designs of Furby for McDonald's.
Every seventh Furby has a blue body, every tenth one has purple hair, and
every twelfth one has green eyes. How many Furbies will have to be
made before one has all three--blue body, purple hair and green eyes?
21. Picnic Problem
Waldo is having a picnic. Unfortunately the store ran out of the box
of plastic silverware that has all three utensils in it. The others come
with 20 forks in one package, 16 spoons in one package, and 17 knives in
one package. How many of each set does Waldo have to buy in order to have
the same amount of each utensil?
22. Sticks Problem
At the end of the summer, the director of the West End Recreation Club
had some gifts from merchants to give to the children. He decided
to make up a game to see who would get the gifts. He lined the children
in numerical order and found that he had 100. He gave the first child
100 sticks. He had him keep one and run down the line and give each
child a stick. They he told the second child to run down the line
and take a stick from every even -numbered child starting with himself.
The third child ran down the line looking only at children who were a multiple
of 3 and did two things. He took a stick from any child who had one
or he gave a stick to any who didn’t. The fourth child did the same
thing with children who were multiples of 4. The game continues until
every child had given or collected sticks. When the game was over,
the director gave a gift to any child who did not have a stick. How
many gifts did the director give out and to which children?
23. Watches Problem
Sixty percent of all watches sold by a large discount store have a
digital display and 40% have an analog display. What is the probability
that exactly four of the next twelve watches sold are digital?
24. Biased Coin Problem
A biased coin when tossed has a probability of 1/3 of turning up heads.
This coin is tossed six times. What is the probability that you will
get at least 2 heads?