What Digit?

A digit is placed in each empty square in the grid so that each row and each column contains the digits 1,2,3,4,5. What digit is placed in the square at the bottom right corner?
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Source: NCTM Mathematics Teacher, November 2006

SOLUTION
Let’s start with the first column by placing 3 in the upper left square because 1,2 are already placed in the first column and 4,5 are already placed in the first row. After that, we place 4 in the third row because 5 is already placed in it. We then place 5 in the last row because it is the only place left.
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We now work on the third column. We place 2 right below 4 because 1,3 are already placed in the second row and 4,5 are already placed in the third column. We place 1 in the last row because that is the only place left. Next we look at the fourth row. We place 4 right next to 2 because 1,2,3 are already placed in it and 5 is already placed in the second column.
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At last we work on the last row. We place 2 right below 4 because 3,4,5 are already placed in the second column and 1 is already placed in the last row. We are left with 3 and 4 to place in the last row. We cannot place 3 next to 1 because 3 is already placed the fourth column. So we place 4 there and 3 in the bottom right corner.
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Answer: 3

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About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , . Bookmark the permalink.

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