PK 2020 Q22
22. In each of the cells, a number is to be written so that the sum of the 4 numbers in each row and in each column are the same.
What number must be written in the shaded cell?
- A 5
- B 6
- C 7
- D 8
- E 9
| 1 | 6 | 3 | |
| 2 | 2 | 8 | |
| 7 | 4 | ||
| 7 |
Pink Kangaroo 2020, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 7
Let \(x\) be the number in the bottom right cell. Then the column total is \(x + 15\). Since each row and column has the same total, we can now find the other missing values. The third column requires \(x\) in its missing cell to make the total up to \(x + 15\). The top row requires \(x + 5\). The second column requires 1. The bottom row is now missing 7, hence this goes in the shaded square. [The other cells in the left column are \(x + 3\) and 4.]
| 1 | x + 5 | 6 | 3 |
| x + 3 | 2 | 2 | 8 |
| 4 | 7 | x | 4 |
| 7 | 1 | 7 | x |
Solution © UK Mathematics Trust, from the PK 2020 solutions.