Problems and Problem Solving - Ministry of Education

Guessing and Testing
Guessing and testing involves selecting likely solutions in accordance with the conditions in
a problem and checking to see if these solutions are correct. This approach can save time if the
options to a solution are few. On the flipside, however, it can be time consuming if there are too
many options that must be eliminated. For example, in order to determine which two consecutive
whole numbers will give a sum of 89, a guess could certainly save time. Consider, though, if
you were asked to determine the number of handshakes that would occur in a room where there
were 200 persons shaking each other’s hands – it would be almost impossible to make appropriate
and intelligent guesses.
Using this method of solving problems does not mean that the problem solver will simply shout
random numbers until they come across the right ones. Each guess should be used to refine
further guesses and to exclude or focus on particular numbers for future guesses. Let us explore
this method using the consecutive whole numbers problem above. After a few guesses students
should realize that:
•y
the numbers must be in the ‘40s’ as any pair of numbers in the ‘30s’ will give a sum that is
more than 60, but less than 80. Furthermore, numbers in the 50s will give sums that are 100 or
more; and
• at some point, consecutive numbers in the ‘40s’ will give a sum that is in the ‘90s’ – all pairs in
which 46–49 is present will give a number in the ‘90s’. For example, 47 and 48 give 95. These
observations are shown below.
The consecutive numbers, therefore, fall between 40 and 45. At this point, the problem solver can
easily identify the requisite numbers as 44 and 45.
Solve a Simpler Problem
This method in problem solving suggests that students take a known problem and make it simpler,
without changing the focus of the problem. Consider the following problem.
What is the last digit in the answer to 2 200 ?
•y
Clearly, no child is expected to multiply 2 by itself 200 times. Additionally, children are not
likely to have a calculator that can produce the solution without using exponents.
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