Grades 3-4 Video Solutions 2021-video 2021 3-4/19

Video Transcription

Problem number 19. The numbers 1 to 9 are placed in the squares shown, with a number in each square.  The sum of all pairs of neighboring numbers are shown. Which number is in the shaded square? A, 4, B, 5, C, 6, D, 7, or E, 8.  We know the sums of the numbers in two squares. For example, these two squares add up to 15, and these two add up to 7.  It's easiest to start with the largest sums. Some of the sums have fewer options of how to make them using two of the numbers from 1 to 9 than others.  For example, the only way to make 15 from the given choices is 7 plus 8, or 6 plus 9.  However, the sum of this box, which is one of the numbers that adds up to 15, and this box is 7. So, the number in this box cannot be 7 or higher, because we don't have a 0 to use.  So, it can't be 7, it can't be 8, it can't be 9, so it has to be 6.  The number in this box will be 6. From there, we know that if 6 and the number in this box add up to 15, the number in this box needs to be 9.  Then, 6 plus 1 makes 7, so this is 1. 1 plus 2 makes 3. 2 plus 7 makes 9. To make 15 again, here we have 7 and 8, then 8 plus 3 makes 11, 3 plus 8 makes 5, and 5 plus 4 makes 9.  At this point, we can double check that we used all the numbers and each one of them only once.  So, we do have 1, 2, 3, 4, 5, 6, 7, 8, and 9, and the number in the shaded box is 7. So, the answer is D, 7.

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