**Skyscrapers Kropki** Put a number between 1-6 inclusive in the grid (the black-bordered square) so that each number appears exactly once in every row/column. Afterwards, interpreting the numbers as heights of buildings, put a number in each cell outside the grid (observer) that tells the number of visible buildings from that position looking into the grid. Taller buildings block shorter ones. For example, if a row has 25341 in that order, an observer from the left will see two buildings (2,5) and from the right will see three buildings (1,4,5).

In addition, if there is a black circle between two cells, one of the numbers in those cells must be exactly twice the other. If there is a white circle between two cells, the two numbers in those cells must differ by one. (There can be either circle between 1 and 2.) The absence of circles doesn’t imply anything.

*Answer key: Enter the unit digits (last digits) of the numbers in the cells in the row/column. Only enter the buildings, not the observers.*

**Difficulty** 4.0/10 • **Target times** 02:00 04:00 07:00 20:00

**Solution** Answer key (highlight →) 563124,362154 • PNG (not uploaded) • ZIP of PDF (not uploaded) • DOCX (not uploaded)

Deception Preview 9: Lines of Circles

Skyscrapers Kropki

Ninth preview puzzle. That ends the Deception preview series. Reminding you that the link is here, and it will start in approximately 31 hours. Good luck!

…yes. This puzzle is posted out of schedule. There’s a long story, but basically Prasanna Seshadri is also going to testsolve this. Or solve this, since it’s official. I don’t know. Whatever. But he wanted the last preview puzzle, and I’m on bed already (yes, this paragraph is hot from the stove), and I don’t have the copy on my phone. So, yeah. Sorry if you find the broken schedule annoying. But earlier never hurts, does it?

About this puzzle itself, it’s supposed to make the shape of P. Or not, I don’t know. I totally forget whether this is intentional or accidental. I toyed with the possibility of lined circles, and this is what happens.

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Good puzzle. This was the easiest one as compared to others which I did for LMI test.