All the dates on this page have faded. Nine shaded cells form a $3\times 3$ block whose dates add up to 135. What is the smallest of the nine dates?

In a $3\times 3$ block the dates are symmetric about the centre, so the sum is 9 × centre: 135 ÷ 9 = 15. The smallest date is top-left: one row up (−7) and one column left (−1): 15 − 8 = 7. (9 is the top-right date; 15 is the centre.)