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#19: It's very natural to intuit this during the contest, but the rigorous proof that the 9 L's must be in the 9 2x2's that are not in in RC36 is by seeing that if in a 3x8 rectangle there are 4 L's, then splitting the 3x8 into 4 3x2's, there must be exactly 1 in each. But then in one of the middle 3x2's, there must be a middle cell filled in. In the 3x2 next to it, the 3 cells filled in must be an entire 1x3 that doesn't touch that center cell of the original rectangle. To finish off, take all 6x8's and up-down and left-right 3x3's. You get that there must be exactly 3 L's in each 2x8 that consists of R12, R45, R78, C12, C45, C78. Together, these rule out RC36.
Now use the the 1 clue and the fact that every RC must contain 2-5 shaded cells to fill in the exact positions.

Ripple+Effect+surely+had+a+rippling+effect+on+my+brain+%f0%9f%98%94

kinda+wish+we+got+90+minutes+for+these

I play best sudoku

I+started+attempting+new+puzzles+that+I+had+never+tried+earlier%2E+I+got+to+taste+some+of+them%2E+Thanks+%F0%9F%91%8D

I+really+enjoyed+those+Ripple+Effects.+Thank+you.

%40jeff10%3A+There+must+be+a+hole+in+your+proof%2C+since+you+can%27t+actually+prove+that+rows%2Fcolumns+3+and+6+are+empty+without+using+the+number+clues%2E++This+pattern+fits%2C+for+example%3A%0D%0A%0D%0A%E2%96%A1%E2%96%A0%E2%96%A0%E2%96%A1%E2%96%A0%E2%96%A0%E2%96%A1%E2%96%A1%2F%0D%0A%E2%96%A1%E2%96%A1%E2%96%A0%E2%96%A1%E2%96%A0%E2%96%A1%E2%96%A1%E2%96%A0%2F%0D%0A%E2%96%A0%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A0%E2%96%A0%2F%0D%0A%E2%96%A0%E2%96%A0%E2%96%A1%E2%96%A0%E2%96%A0%E2%96%A1%E2%96%A1%E2%96%A1%2F%0D%0A%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A0%E2%96%A1%E2%96%A1%E2%96%A0%E2%96%A0%2F%0D%0A%E2%96%A0%E2%96%A0%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A1%E2%96%A0%2F%0D%0A%E2%96%A0%E2%96%A1%E2%96%A1%E2%96%A0%E2%96%A1%E2%96%A0%E2%96%A1%E2%96%A1%2F%0D%0A%E2%96%A1%E2%96%A1%E2%96%A0%E2%96%A0%E2%96%A1%E2%96%A0%E2%96%A0%E2%96%A1%0D%0A%0D%0AI+wish+I+could+offer+a+full+proof+that+the+puzzle+solution+is+unique%2C+but+I+don%27t+have+one%21

Edited by csell 2025-03-17 2:47 AM

Very+nice+round!

Whoops.+Though+I+think+that+we+can+then+prove+that+the+best+you+can+do+is+10+shaded+squares+in+a+3x8%2c+in+which+the+configuration+you+provided+(and+rotations+and+reflections)+is+the+only+one+that+works%2c+but+it+will+never+fit+the+number+clues.

%f0%9f%a4%af+Place+by+Unique+products+was+a+nice+one+%0a%0aHappy+to+solve+one+Mukkonn+Enn+%3a)