SEMI-SPOILERS
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STARTING SEQUENCE
fill sat - day sum
fill 12,13,16,17 - one rest that week, no 5d
rest 10 - 10 filled would lead to two 4d on week3
fill 8 - a rest there would need to fill 5–7, which would make a 4d there, when a 4d is needed on week3
rest 19 - filling 19 would force 2 4d on week3
rest 6 - 20 or 27 must be rest (day sum), can't both be rest since too many 2x rests
BASIC RULE IMPLICATIONS
4+3*2+2*3+4 = 20 total work days
9 events
31 calendar days
11 empties, which means 2 extra empties, either surrounding or between calendar units
4d can't be on week1 (4d as to be on week2 or week3), week4 (too many gaps), or week5 (week sum)
3d can't be on week5 (too many empties created)
1 gap only on week3 (week sum)