Discussion
Consider the following matrix :
| 3 | 8 | 10 | 2 | ? | 1 |
| 6 | 56 | 90 | 2 | 20 | 0 |
What is the missing number at '?' in the matrix ?
Answer: A
The missing number is 5.
Each number in the second row is the top number times one less than itself, \(n(n - 1)\):
\[ \begin{aligned} 3 \times 2 &= 6,\quad 8 \times 7 = 56,\quad 10 \times 9 = 90 \\ 2 \times 1 &= 2,\quad 1 \times 0 = 0,\quad 5 \times 4 = 20 \end{aligned} \]
So the top number over 20 is 5. 0 gives 0, 7 gives 42, and 3 gives 6.
Recognising products of consecutive integers (2, 6, 12, 20, 30, 42, 56, 72, 90) makes such matrices quick to solve.
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