Chinese Remainder Theorem (韩信点兵) “The Problem of 6 Professors”

How to formulate this problem in CRT (Chinese Remainder Theorem, aka“韩信点兵”dated since 3rd century in China.) ?

Let d = week days {1, 2, 3, 4, 5, 6, 7} for {Monday (Prof M), tuesday (Prof t), Wednesday (Prof W), Thursday (Prof T), Friday (Prof F), saturday (Prof s), Sunday (Prof S)}

d : 1 2 3 4 5 6 [7] 1 2 3 4 5 6 [7] 1 2
M: m 0 m 0 m 0 [m] ==> fell on 1st sunday
t: - t 0 0 t 0 [0 ] t 0 0 t 0 0 [t ] ==> fell on 2nd sunday
W: – - w 0 0 0 [w] 0 0 0 w 0 0 [0] ==> fell on 1st sunday
T: - - - T T T [T] ==> fell on 1st sunday (TRIVIAL CASE!)
F: - - - - f 0…