Problems and Problem Solving - Ministry of Education

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Once we get to the $5 coin, we will find that we have already combined it with the 10¢, 25¢
and $1 coins, thereby exhausting all possible combinations.
So there are six possible monetary values when two coins are combined.
Combinations of three coins
To determine all the combinations of three coins we will use the combinations of two coins we
had previously found as a base and build on it using a method similar to the one used in that section.
This time around, however, rather than keeping one coin constant we will keep one pair of
coins constant and vary the third coin with which they are combined.
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The first pair we will hold constant is 10¢ + 25¢. This will be combined with each of the two
remaining coins.
10¢ + 25¢+$1 10¢ + 25¢+$5
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We will then move to 10¢ + $1. Here we will need to exercise some caution, keeping in mind
that we would have already seen the combination of 10¢ + 25¢.
10¢ + $1+ $5
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Next, we will look at 10¢ + $5. By now we would have seen that there will be no new combinations
as these have already been explored in the previous cases.
Similarly, we will examine 25¢+ $1. Once we have done this we should realize that we have
exhausted all possible combinations.
25¢+ $1 +$5
So here we have four possible monetary values when three coins are combined.
Combinations of four coins
Immediately we can appreciate that there is only one set of four different coins, and need not
reduce the combinations that we had for the previous cases.
$1 + $5 + $10 + $20
In all, we have a total of 15 possible monetary values when we have four coins.
We can, therefore, put these results in a table as shown below.
22 PROBLEMS AND PROBLEM SOLVING
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