A: 69 ÷ 3 = 23, and the adjacent three numbers are 22, 23 and 24.

Since 1 is Monday, 22, 23 and 24 are Monday, Tuesday and Wednesday.

B:54÷3= 18, and the three adjacent numbers are 17, 18 and 19.

Since 1 is Monday, 17, 18 and 19 are Wednesday, Thursday and Friday.

C:27÷3=9, and the adjacent three numbers are 8, 9 and 10.

Since 1 is a Monday, 17, 18 and 19 are Mondays, Tuesdays and Wednesdays.

In short:

The sum of three adjacent numbers or a multiple of three.

And d is obviously not a multiple of 3.