Developing Problem Solving Skills
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School
Northern Virginia Community College *
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Course
154
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
5
Uploaded by BaronArmadillo3003
Developing Problem Solving Skills
Activity 2 -- Problem Solving
Name: Erick Membreno
MTH154
Date: 02-18-3023
Instructions for the Activity:
First, save this file and rename it to
‘
ACTIVITY_2_LASTNAME_FIRSTNAME.DOCX’
inserting
your own name. Use Microsoft Word to type your answers into the space following each
problem. When finished, upload your file into Canvas.
If you convert this doc into some other
format to work on it, you MUST upload it with your answers in either Word ( .docx ), or PDF (
.pdf) formats. If you print it out and write in your answers, you must scan it to a PDF format or
JPG or PNG image formats to upload it.
These problems all involve logic and thinking clearly.
Some require simple math calculations.
The key is to first read the question carefully because the wording of the problem is significant.
Then relate the question to the facts you are given to analyze and solve it. Each problem is
worth 5 points.
1. (Easy) Read carefully.
If there are 12 one-cent stamps in a dozen, how many
two-cent stamps are there in a dozen? There are 12 two cents. It is basically the
same.
2. (Easy) Whose egg?
If Mr. Jones’ rooster laid an egg in Mr. Gomez’ yard, who
owns the egg? Explain.
Rooster do not lay eggs. None of them own the egg.
3. (Medium) Read carefully.
The butcher is six foot four inches tall, and he wears
size 14 shoes. What does he weigh?
It weighs meat.
4. (Medium) Read carefully.
Is it legal for you to marry your widow's sister? Explain.
No because for me to marry my widow’s sister I’ll have to be alive. A widow means
the husband is dead.
5. (Easy) Read carefully.
I am the brother of the blind fiddler, but brothers I have
none. How can this be? The blind fiddler must be a woman because the brother
states he has no brothers.
6. (Easy) Read carefully.
Anna had six apples and ate all but four of them. How
many apples were left?
4 of them.
7. (Medium) Banquet counting.
There were 100 basketball and football players at
a sports banquet. Given any two athletes, at least one was a basketball player. If at
least one athlete was a football player, how many football players were at the
banquet?
One football player.
8. (Hard) Fathers and sons.
“Brothers and sisters I have none, but that man's
father is my father's son.”
Who is “that man”?
He is my nephew.
9. (Hard) From the eighth century.
A man arrived at the bank of a river with a
goat, a wolf, and a head of cabbage. His boat holds only himself and one of his
possessions. Furthermore, the goat and the cabbage cannot be left alone, and the
wolf and the goat cannot be left alone. What is the minimum number of trips needed
for the man to cross the river with his three possessions? Explain how it is done.
The minimum number of trips is 4 because he would have to take each one of them
in every trip since they can’t be left alone together.
10. (Medium) Buy and sell.
Kelly bought a horse for $500 and then sold it for $600.
She bought it back for $700 and then sold it again for $800. How much did she gain
or lose on these transactions?
She only gained $100.00.
11. (Medium) Rising tide.
A rope ladder hanging over the side of a boat has rungs
one foot apart. Ten rungs are showing. If the tide
rises
five feet, how many rungs
will be showing?
5 rungs.
12. (Medium) Chocolate demographics.
Suppose one-half of all people are
chocolate eaters and one-half of all people are women. (i) Does it follow that
one-fourth of all people are women chocolate eaters? (ii) Does it follow that
one-half of all men are chocolate eaters? Explain.
(12 (12).
It does not follow.
Because ¼ of all the people are women chocolate eaters. If it states that ½ of the
total people are women, it does not mean that they all eat chocolate I am assuming.
(ii) Same thing for men, it does not follow that ½ of men are chocolate eaters.
13. (Medium) Rolling quarters.
Two quarters rest next to each other on a table.
One coin is held fixed while the second coin is rolled around the edge of the first
coin with no slipping. When the moving coin returns to its original
position
, how
many times has it revolved?
It revolves twice.
14. (Easy) Mixed apples.
Three kinds of apples are all mixed up in a basket. How
many apples must you draw (without looking) from the basket to be sure of getting
at least two of one kind?
4 Apples
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15. (Easy) Socks in the dark.
Suppose you have 40 blue socks and 40 brown
socks in a drawer. How many socks must you take from the drawer (without looking)
to be sure of getting:
(i) a pair of the same color- 3 because I’ll have a pair of socks either blue or
brown
and
(ii) a pair with different colors? 41.
16. (Hard) Clock chimes.
If a clock takes 5 seconds to strike 5:00 (with 5 equally
spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced
chimes)?
10 seconds.
17. (Medium) Optimal grilling time.
A small grill can hold two hamburgers at a
time. If it takes five minutes to cook one side of a hamburger, what is the shortest
time needed to grill both sides of three hamburgers?
15 minutes
18. (Hard) Coin weighing problem.
There are 8 identical looking coins, but 1 is
counterfeit and is lighter than the others. How do you find the light counterfeit coin
among eight coins using only two weighing? Assume that a 2-pan balance scale is
used. A weighing consists of putting a sample of coins on each pan of the balance
and observing whether the pans balance or whether one pan weighs more than the
other pan. A balance scale has no dial to indicate the actual weight in ounces.
(18).
I am assuming if you put one coin on and measure the weight and second coin on and
measure it and if one of the coins is lighter, it is the counterfeit. You keep doing it until you find
the lighter one since coins are heavier than a counterfeit.
19. (Hard) Family counting.
Suppose that each daughter in your family has the
same number of brothers as she has sisters, and each son in your family has twice
as many sisters as he has brothers. How many sons and daughters are in the
family?
I believe it is 3.
20. (Hard) A bet.
Alex says to you, “I'll bet you any amount of money that if I shuffle
this deck of cards, there will always be as many red cards in the first half of the deck
as there are black cards in the second half of the deck.” Should you accept his bet?
Explain.
No because no matter how many times he shuffles the deck it will always remain
the same.
21. (Medium) Book order.
Five books of five different colors are placed on a shelf.
The orange book is between the gray and pink book, and these three books are
consecutive. The gold book is not first on the shelf and the pink book is not last. The
brown book is separated from the pink book by two books. If the gold book is not
next to the brown book, what is the complete order of the five books?
Pink, Orange, Gray, Brown, and Gold.