Problem Solving In Mathematics
Make a Systematic List
Often a systematic list or table can make the search for a solution to a problem much easier. For instance, in how many ways can you pile 25 marbles into 3 piles with an odd number in each pile? By organizing a list, all solutions can be found.
| Pile 1 | Pile 2 | Pile 3 |
|---|---|---|
| 1 | 1 | 23 |
| 1 | 3 | 21 |
| 1 | 5 | 19 |
| 1 | 7 | 17 |
| . | . | . |
| . | . | |
| . | . | . |
Other problems involving systematic lists or tables are given below.
Here are the other problem solving strategies:
Other Make a Systematic List Problems
Day 16 - Take 25 marbles. Put them in 3 piles so an odd number is in each pile. How many ways can this be done?
Day 17 - A rectangle has an area of 120 sq. cm.. Its length and width are whole numbers. What are the possibilites for the two numbers? Which possibility gives the smallest perimeter?
Day 18 - The product of two whole numbers is 96 and their sum is less than 30. What are possibilities for the two numbers?
Day 19 - Jamie and Lynn each worked a different number of days, but each earned the same amount of money. Use the following clues to find how many days each worked: - Jamie earned $ 15 a day. - Lynn earned $ 10 a day. - Lynn worked 5 more days than Jamie.
Day 20 - Lonnie has a large supply of quarters , dimes, nickels, and pennies. In how many ways could she make change for 50 cents?
Day 41 - How many different four-digit numbers can be formed using the digits 1, 1, 9, and 9?
Day 42 - Two different prime numbers are selected at random from the first ten prime numbers. What is the probability that the sum of the two primes is 24?
Day 43 - Which is greater : $ 5.00 or the total value of all combinations of three coins you can make using only pennies, nickles, dimes, and quarters?
Day 44 - "Chicken Chunkettes" come in boxes of 6, 9, and 20. What is the largest number of chunkettes you can't buy?
Day 45 - In how many different ways is it possible to score 15 points in basketball?
Day 66 - A basketball player is on the line to shoot a 1 and 1 freethrow. If the player's free throw average is .750, what is the probability that she will score exactly one basket?
Day 67 - Several sets of three different numbers whose sum is 15 can be chosen from 1, 2, 3, 4, 5, 6, 7, 8, 9. How many of these sets contain a 5?
Day 68 - How many positive integral factors does the number 720 have?
Day 69 - A football team boasts that all the numbers on the jerseys are prime numbers under 100. What is the largest number of players the team could have?
Day 70 - A three digit number is selected at random from all three digit numbers 100 - 999. What is the probability that the number is a perfect square?
Day 91 - How many four digit numbers N have the following properties? (1) the sum of the digits of N is the same as the number obtained by deleting the last two digits of N. (2) the sum of the digits of N equals the product of the last two digits of N.
Day 92 - A social club contains 7 women and 4 men. The committee wants to select a committee of 3 members to represent it at the state convention. How many of the possible committees that could be chosen contain at least one man?
Day 93 - How many distinct isosceles triangles having sides of integral length and a perimeter of 113 are posssible?
Day 94 - How many different secret code words can be made using three stars and two dashes in each word?
Day 95 - If you make $ 1000 every time the hands of a clock form a 90-degree angle, how much would you make in 24 hours?
Day 116 - How many decimal numerals are made up of the digits 1, 2, 3, 4, 5, each used at most once, and are also multiples of 8?
Day 117 - In how many ways can eight dollars be changed into dimes and/or quarters?
Day 118 - Radio stations use three or four letters for their call letters. The first letter must be a W or a K. How many different call- letter strings are possible if no letter may be repeated within a string?
Day 119 - A number is chosen at random from the following : .25, .5, .75, .8, 1, 2, 2.2, 3, 4, 9.7 What is the probability that its reciprocal is greater than one?
Day 120 - Myrtle has two white balls, two black balls, and two boxes. She may place the balls in the boxes in any way that she pleases. Her husband will then pick a box without looking into it, and with his eyes closed, pick out a ball. If he draws a white ball, the couple wins $ 500. How should Myrtle arrange the balls to maximize the probability of winning?
Day 141 - If each of these three operation signs, +, -, and x is used exactly once in the blanks in the expression 5 ___ 4 ___ 6 ___ 3 then how many different final values can you make?
Day 142 - How many three - digit numbers can be formed from the digits 0, 1, 2, 3, and 4 if no repetitions are allowed?
Day 143 - Using a deck of 52 cards, how many 5 card poker hands that contain 4 aces can you construct? Assume that no cards are wild.
Day 144 - The sum of three numbers is 98. The ratio of the first to the second is 2 to 3, and the ratio of the second to the third is 5 to 8. What is the second number?
Day 145 - A salesperson wants to rent a car for one day. Rental agency A charges $ 35 per day plus $ .20 per mile driven. Rental agency B charges $ 30 per day plus $ .25 per mile driven. Should she rent from Agency A or Agency B to get the best rate?
