Chapter One:
Problem Solving
MATH111
Friday, January 16
Problem Solving
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Strategies for problem solving
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Guesswork
Logic and intuition
Simplify the problem
Think “outside the box”
Problem #1
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A farmer has exactly 100 feet of fencing. He
wants to construct a rectangular fence for his
23 cows that will maximize the grazing area.
What should be the length and width of his
fence?
Some Trial and Error
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2 Length + 2 Width = 100 feet
So, Length + Width = 50 feet
If Length = 10, Width = 40, Area = 400 sq ft
If Length = 20, Width = 30, Area = 600 sq ft
If Length = 30, Width = 20, Area = 600 sq ft
If Length = 35, Width = 15, Area = 525 sq ft
Answer
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His fence should be a square with length and
width of 25 feet.
Area = length x width = 25 x 25 = 625 sq feet
Problem #2
 56
biscuits are to be fed to ten
pets. Each pet is either a cat or a
dog. Each dog is to get 6 biscuits
and each cat is to get 5 biscuits.
How many dogs are there?
Solution Using Algebra
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X = Number of Dogs
Y = Number of Cats
X + Y = 10, So X = 10 - Y
6X + 5Y = 56
6(10-Y) + 5Y = 56
60 – 6Y + 5Y = 56
60 –Y = 56
-Y = -4, Y = 4, So X = 6
Problem #3
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For his birthday, Adam went to the store to
purchase a brand new 5 foot fishing pole. To
get home, he needed to take the bus, but the
driver told Adam that he could not board the
bus with the fishing pole because objects
longer than 4 feet were not allowed on the
bus.
#3 Continued
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Adam’s friend Sarah agreed to help out by
providing him with something to help. With
her help, Adam was able to board the bus
with his pole without breaking or bending the
bus-line rules or the pole. How did he do it?
Problem #4
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Superhero cop John McClane (Bruce Willis)
returns in Die Hard 3: DIE HARD WITH A
VENGEANCE. Freshly expelled from the
NYPD, McClane encounters a number of
threatening phone calls from a terrorist
calling himself Simon. Simon tests
McClane’s wits, and allows him the chance to
stop each bomb by solving a riddle. In
addition to using his previously learned antiterrorism tactics (DIE HARD, DIE HARD 2) ,
McClane enlists an angry store clerk, Zeus
(Samuel L. Jackson) to decipher Simon’s
tricky enigmas.
Die Hard: The Fountain Riddle
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McClane and Zeus are at a fountain in the
park and need to measure out exactly 4
gallons of water and place it on a scale to
stop the bomb. The problem is they have
only a 3 gallon container and a 5 gallon
container. If the bucket does not hold exactly
4 gallons, the bomb will explode. How do
they save the city?
Problem #5
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You are a brave knight and want to rescue a
damsel in distress from a nearby castle. The
castle is surrounded by a 20ft wide square
alligator-infested moat on all sides and no
drawbridge existed. The only resources you
can locate are two sturdy boards, each 19
feet in length and 8 inches wide.
Castle Continued
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You have no nails, screws, saws, glue, or
any other method of joining the two beams to
extend their length. Can the damsel be
saved?
Problem #6
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Mom and Dad and two kids have to cross a
river, and they find a boat, but it is so small
that it can only carry one adult or two kids.
Luckily, both of the kids are good rowers, but
how can the whole family get across the
river?
Problem of the Day
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Two rooms are connected by a hallway that
has a bend in it so that it is impossible to see
one room while standing in the other. One of
the rooms has three light switches. You are
told that exactly one of the switches turns on
a light in the other room, and the other two
are not connected to any lights.
POD continued
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You are allowed only one trip to the other
room to check the light. How do you know
which switch turns on the light?