1) When certain numbers are placed in the empty boxes, the sum of the three numbers in each of the three rows, three columns, and two diagonals is the same. What number should be placed in the center box?
2) I am less than 6 feet tall but more than 2 feet tall. My height in inches is a multiple of 7 and is also 2 inches more than a multiple of 6. What is my height in inches? 3) The square below is divided into four congruent rectangles. The perimeter of each of the four congruent rectangles is 25 units. How many units are there in the perimeter of the square? Solutions 1) Since the sum of the three numbers in each diagonal is the same, and since they have the same middle number, the sum of each pair of numbers in opposite corners must be the same: 9 + 13 = 5 + ?. Clearly ? = 17. The bottom row now has a sum of 33. The middle number must be 11. 2) List multiples of 7 greater than 24 and less than 72. Also list the multiples of 6 which are less than and closest to each of the corresponding multiples of 7. 3) Each of the four congruent rectangles has a perimeter equivalent to 2 1/2 sides of the square. Since the length of 2 1/2 sides = 25 units, then, by doubling, we get the length of 5 sides = 50 units. Clearly, the length of one side is 10 units. Therefore the perimeter of the square is 40 units.
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