Chapter One:Problem Solving

MATH111

Friday, January 16

Problem Solving

Strategies for problem solving– Guesswork– Logic and intuition– Simplify the problem– Think “outside the box”

Problem #1

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

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

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

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

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

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

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 anti-terrorism 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

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

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

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

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

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

You are allowed only one trip to the other room to check the light. How do you know which switch turns on the light?