A science museum designed a digital security lock using a \(4 \times 4\) magic square. The lock opens only if every row, column and diagonal gives the same magic sum. During maintenance, one number disappeared from the display. The engineer asked the students to determine the missing number by analysing the pattern rather than trying random values.
Magic square:
| 16 | 2 | 3 | 13 |
| 5 | 11 | \(x\) | 8 |
| 9 | 7 |
6
|
12 |
| 4 | \(y\) | \(z\) | 1 |
Based on the above information, answer the following questions.
(i) What is the magic sum?
(ii) What number should replace \(x\)?
(iii) What number should replace \(y\)?
(iv) What is the sum of \(y\) and \(z\)?