Problem Solving In Mathematics
Simplify the Problem
Suppose we each have a bag of pennies. We take turns putting them on a rectangular table. No penny can hang over the edge and no pennies can overlap although they can touch. Whoever puts a penny in the last space available wins all the pennies. Would you want to play first or second? How would you play to win? What if you had a table only big enough to hold one penny?
That's pretty easy. You play first and win.
What about a two-penny sized table? Would you go first or second and where would you place your penny to guarantee a win?
How about a three-penny sized table?
A four-penny sized table?
(hint: what would happen if you placed your penny in the middle?)
Do you see that by simplifying the problem you can find a strategy to win every time?
Here are the other problem solving strategies:
- Guess and Check
- Look for a Pattern
- Make A Systematic List
- Make A Drawing Or Model
Other Simplify the Problem, Problems 
Day 21 - Suppose we each have a bag of pennies. We take turns putting them on a rectangular table. No penny can hang over the edge and no pennies can overlap although they can touch. Whoever puts a penny in the last space available wins all the pennies. Would you want to play first or second? How would you play to win?
Day 22 - How many line segments can be drawn through each of 15 points? No three points are in a straight line.
Day 23 - Find the product: ( 1 - 1/2)(1 - 1/3)(1 - 1/4)......(1 - 1/98)(1 - 1/99)(1 - 1/100) = ?
Day 24 - Find the sum: 1/1x2 + 1/2x3 + 1/3x4 + ..... +1/98x99 + 1/99x100 = ?
Day 25 - Ten strangers attend a meeting. As introductions are made, each person shakes hands with all the others. How many handshakes occur?
Day 46 - If eighteen ounces of dough are used to make a sixteen-inch pizza, how many ounces are used for a twenty-inch pizza?
Day 47 - List these numbers in increasing order; 2800, 3600, 5400, 6200
Day 48 - Jeremy travels from A to B at 2 minutes per mile and returns over the same route at 2 miles per minute. Find his average speed, in miles per hour, for the whole trip.
Day 49 - A ten meter pole and a forty meter pole are placed fifty meters apart on flat ground. Two nonsagging ropes join the top of one pole to the bottom of the other pole and vice versa. Calculate the height from the ground of the point of intersection of the ropes.
Day 50 - Four numbers are written in a row. The average of the first two numbers is 7, the average of the middle two numbers is 2.3, and the average of the last two numbers is 8.4. What is the average of the first number and the last number?
Day 71 - How many squares are in this picture?
Day 72 - Solve for x: 
Day 73 - A certain king sent 30 men to plant trees. If they can set out 1000 trees in 9 days, how many days would it take for 36 men to set out 4400 trees?
Day 74 - A dog chasing a rabbit, which has a lead of 150 feet, jumps 9 feet for every time the rabbit jumps 7. In how many leaps does the dog overtake the rabbit?
Day 75 - Ten people are seated around a circular table. Each person shakes hands with everyone else except the people who sat on either side. How many handshakes take place?
Day 96 - A wagon train had 96 wagons , each carrying the same number of people. When 12 wagons broke down, each of the other wagons had to carry one more person. How many people were in each wagon originally?
Day 97 - What was a walker's average speed if she completed a trip around the square city block shown here?
Day 98 - In the 1973 Belmont Stakes, Secretariat covered 12 furlongs in 2 minutes, 24 seconds. What was his speed in miles per hour?
Day 99 - A crowd watching a parade fills the sidewalks on both sides of the street for a distance of 2 miles. The sidewalks are 10 feet deep and an average person needs 4 square feet to stand on. A good estimate of the crowd is : (a) 25,000 people (b) 50,000 people (c) 100,000 people (d) 250,00 people (e) 500,000 people
Day 100 - A school has 1200 students. Each student takes 5 classes a day. Each teacher teaches 4 classes. Each class has 30 students and 1 teacher. How many teachers does the school have?
Day 121 - How many whole numbers between 100 and 400 contain the digit 2?
Day 122 - A cake has three circular tiers; each is 8 cm. high. The tiers have diameters of 60 cm., 48 cm., and 36 cm.. What is the surface area to be covered by frosting? There is no frosting between layers.
Day 123 - How many different routes can be traced from point A to point B if the movement cam only be horizontal or vertical?
Day 124 - In a 10 team conference where each team plays each other team at home, how many conference games are played in a season?
Day 125 - The density of wood of a pine tree is 35 lbs/ft3.The tree is 72 feet high and the diameter of the base is 3 ft.. Ten percent of the weight of the tree is contained in the branches and foliage. If the trunk of the tree is a right circular cylinder, estimate the weight of the tree ( above ground ).
Day 146 - A dart is thrown at the square target shown. Assuming that the dart hits the target randomly, what is the probability that it will be in the shaded region?
Day 147 -
If 2 + 3 + 4 + ... + 1990 + 1991 + 1992 = 3N,
then N = ?
Day 148 - 66 + 66 + 66 + 66 + 66 + 66 = ? (A) 66 (B) 67 (C) 366 (D) 636 (E) 3636
Day 149 - List from least to greatest: 2121, 955, 788
Day 150 - If
, find (3 * 48)*9.
