Problem Solving - Solve a Simpler Problem

	Problem Solving Strategy ~ Solve a Simpler Problem ~

Content

	Process Problem 1
	Process Problem 2
	Process Problem 3
	Problem Worksheet

Process Problem 1

Sometimes a problem is too complex to solve in one step. When this happens, it is often useful to Simplify the problem by dividing it into cases and solving each one separately.

Use the hints provided to solve each of the following problems.

1. How many palindromes are there between 0 and 1000?
(A palindrome is a number like 525 that reads the same backward or forward.)

Simplify the problem. Find the number of one, two, and three digit palindromes separately.Make a list. Use the list I've started, and look for a pattern!

a. How many of the numbers 1 through 9 are palindromes?

All nine numbers are palindromes.

b. How many of the numbers 10 through 99 are palindromes?

11
22 nine
:
:
99

Make a List

c. Find the number of palindromes from 100 through 999.

1 0 1	2 0 2	.........	9 0 9
1 1 1	2 1 2	.........	9 1 9
1 2 1	2 2 2	.........	9 2 9
1 3 1	:		:
: :	: :		: :
1 9 1	2 9 2	.........	9 9 9

9 columns x 10 palindromes/column = 90
90 palindromes from 100- 999

Use the list I've started, and look for a pattern!

d. What is the answer to this original question?

There are 108 palindromes between 0 and 1000

Process Problem 2

A pie can be cut into seven pieces with three straight cuts. What is the largest number of pieces that can be made with eight straight cuts?

Cuts	1	2	3	4	5	6	7	8
Pieces	2	4	7	11	16	22	29	37

simpler1.jpg (12771 bytes)

Process Problem 3

Tony's restaurant has 30 small tables to be used for a banquet. Each table can seat only one person on each side. If the tables are pushed together to make one long table, how many people can sit at the table?

Strategies involved

Simplify the problem
Draw a picture
Make a table
Look for a pattern

No. of tables	No. of people
2	6
3	8
4	10
5	12
6	14
:	:
:	:
30	62

simpler2.jpg (11117 bytes)

Pattern: 2 times the number of tables plus 2 ===> 2 x 30 = 60 ===> 60 + 2 = 62

62 people can sit at the table.

Process Worksheet: Solve a Simpler Problem

1. How many squares are in this figure?

2. How many triangles are there in this figure?

simpler3.jpg (2961 bytes)

3. A total of 28 handshakes were exchanged at a party. Each person shook hands exactly once with each of the others. How many people were present at the party?

4. If a student were to calculate the product of all natural numbers from 1 to 25 inclusive (i.e., 1 x 2 x 3 x 4 x ….x 24 x 25 ), how many zeros would there be at the end of this product?

5. Find the thickness of one page in your mathematics text book.

6. Mike is paid for writing numbers on pages of a book. Since different pages require different numbers of digits, Mike is paid for writing each digit. In his last book, he wrote 642 digits. How many pages were in the book?