Grades 7-8 Video Solutions 2023-2023_7-8

Video Transcription

Question 14. Matchsticks can be used to write digits as shown in the diagram. How many different positive integers can be written using exactly 6 matchsticks in this way?  First, let's start off with eliminating the numbers that will be useless to us. We can start off by getting rid of 0, since it requires 6 matchsticks to create.  0 is not a positive integer, and we would have no remaining matchsticks to make any other digits, so we can block this out.  Next, we look at the digit 8. This requires 7 matchsticks. We do not have 7 matchsticks, so we can cross this out as well.  Next, we can cross out some more digits. The ones that require 5 matchsticks each will be removed, since there are no digits that require only 1 matchstick, so let's block those out as well.  We are left only with digits 1, 4, 6, 7, and 9. Digits 6 and 9 both require 6 matchsticks, so we can make the number 6 and the number 9.  Now we can disregard these. We are left with 1, 4, and 7.  The digit 1 requires 2 matchsticks. The digit 4 requires 4 matchsticks, so together they require exactly 6 matchsticks, so we can make the numbers 14 and 41.  The digit 7 requires 3 matchsticks, but with this, we can make the number 77.  Finally, since 1 requires 2 matchsticks, we can use 6 matchsticks to make 3 ones, making the number 111.  And with this, the number of different positive integers that we can make using 6 matchsticks is going to be 6. See?

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