Jenny decided to enter numbers into the cells of a 3 × 3 table so that the sum of the numbers in all four possible 2 × 2 cells will be the same. The numbers in three of the corner cells have already been written, as shown. Which number should she write in the fourth corner cell?
A 0 B 1 C 4 D 5 E 6
B
Let the numbers in the centre left cell and the centre right cell be x and y and let the number in the lower left corner be z, as shown in the diagram. Since the sum of the numbers in all four possible 2 × 2 cells should be the same, by considering the top left 2 × 2 cell and the top right 2 × 2 cell, since the top two cells in the central column are common, we have 2 + x = 4 + y and hence x = y + 2. Similarly by considering the bottom left 2×2 cell and the bottom right 2×2 cell where the lowertwo cells in the central column are common, we have z + x = y + 3 and hence z + y + 2 = y + 3,which has solution z = 1. Therefore the value of the number in the fourth corner cell is 1.
Be up-to-date with our recent updates, new problems and answers!
Ask about our courses and offerings, and we will help you choose what works best for you.
