Question 20. Rhea wants to complete the puzzle shown so that each row and each column contains the numbers 1, 2, 3, and 4 exactly once. She wants to place the numbers so that the greater than and less than symbols give a correct relationship between the two values either side of them. The symbols work in all directions, as shown in the example. What numbers should she place in the gray circle? First, let's look at the circles to the right of the 3. Notice how the circle directly to the right of the 3 must be less than 3, and the number below that must be even less, which only gives us one way to place the numbers here. We have to place a 2 to the right and a 1 below that. Now, let's look to the left of the 3. We can see that the circle here must be less than 3, but since we already used a 2 in this row, the circle must be a 1. Now, let's look at the circle below the 3. We can see that its value should be less than 3, and since 1 is already used in this row, it must be 2. Finally, let's look at the circle above the 3. Once again, the symbol tells us that it has to be less than 3, and since 2 is already used in this column, this circle must have a 1. Each row and column must have a 1, which means our first column and bottom row still need a 1. We can see that the 3 1s we've placed earlier take up all the other rows and columns, which means we must place a 1 in the bottom left circle, which happens to be the gray circle. Therefore, our answer is 1.

puzzle

numbers

logic

placement

deduction