Question

Fill in the blank

$\begin{array}{ccc}0& 80& 24\\ ....& 48& 35\\ 15& 63& 3\end{array}$

Answer 1

Arrange can notice that the differences are 3, 12, 9, 11, 13, 15 and 17. however, between the second and third numbers, the difference is 12. Split this as 5 + 7. The missing number is 3 + 5 = 8 (verification; 8 + 7 = 15 which is the next number)
You can also solve the above problem by applying the algebraic formula, $n^2-1$.
$1^2-1=0;2^2-1=3$
$4^2-1=15;5^2-1=24$
$6^2-1=63;7^2-1=48$
$8^2-1=633;9^2-1=80$