Friction
(Published on 14. August 2026, 17:02 by mathpesto)
Rules:
Normal sudoku rules apply.
Yin Yang: Shade some cells in the grid so that all shaded cells are orthogonally connected and all unshaded cells are orthogonally connected. A 2x2 area cannot be fully shaded nor fully unshaded.
Negators: A digit’s value in an unshaded cell is the digit itself and a digit’s value in a shaded cell is the digit’s negative. For example, a “3” in an unshaded cell is 3 and in a shaded cell is –3.
Skyscraper: Values of cells represent the elevation above/below sea level. Clues outside the grid equal the amount of numbers seen in that row/column from that vantage point. For example, suppose a row contains the values –3, 2, –8, 5, 4, 7, -6, –1, –9. Then 4 values are seen from the left (–3, 2, 5, 7) and 3 values are seen from the right (–9, –1, 7).
Solve online:
Solution code: Digits in unshaded cells (positives) in Row 7
Comments
on 17. September 2026, 22:24 by Nemefish
Tricky but excellent. By the time I finally got the rhythm the puzzle was sadly over.
on 4. September 2026, 18:09 by KeenanN
This puzzle made my day. What an incredible work of art you have shared with us. Thank you, mathpesto!
on 20. August 2026, 08:27 by Piatato
Splendid!
on 16. August 2026, 19:35 by rubencubed
loved that the yin-yang coloring was needed until the very end :D
on 16. August 2026, 10:41 by Christounet
Excellent! Thanks :)
on 15. August 2026, 19:57 by Snookerfan
Very nice, excellent setting! Unexpectedly intuitive, I solved it in a 2.5 to 3 star time. Thanks!
on 15. August 2026, 18:55 by Franjo
Thank you very much for creating and sharing this awesome YY-hybrid. Amazing how this works!
on 15. August 2026, 17:03 by marcmees
Very nice. Thanks
on 15. August 2026, 13:11 by wuc
Never imagined that a skyscraper puzzle could be so much fun. Awesome puzzle thx.
on 15. August 2026, 12:19 by at_ing
太好玩辣！
的确是环环相扣，阴阳的推论和摩天大楼有机结合。并且作者设计了很多“巧合”般的限制，从而能锁定唯一数字，有和作者对话的感觉，做起来很爽。
on 15. August 2026, 12:00 by Jessione
Beautiful puzzle!
on 15. August 2026, 11:45 by amirs
Beautiful!!
on 15. August 2026, 10:58 by Piatato
The rules seem quite unclear to me. How am I supposed to know if a clue sees increasing or decreasing digits? Does it have to do with which colour it sees first, or which side of the grid it's on, or is it supposed to be ambiguous? What does the sea have to do with anything?
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@Piatato: With regular skyscrapers, you are at sea level (or 0 elevation or ground) and looking up, therefore only seeing increasing values. With this variation, you are still looking up and only seeing increasing values, but starting below sea level. As another example, if a row contains -8, -5, -7, 3, 4, -9, 2, 1, -6, from the left it sees -8, -5, 3, 4 and from the right it sees -6, 1, 2, 4. -Math Pesto
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I completely hallucinated one of the sides seeing decending digits. Thanks for the help and patience!
on 15. August 2026, 10:16 by crosslegged
Very fun yin yang variant.
on 15. August 2026, 08:14 by damo_89
Beautiful. Really impressive being able to get unique grid and shading with just outside skyscrapers.
on 15. August 2026, 01:55 by Ramez
What a fresh approach to skyscrapers! Loved it! I hope Simon will have lots of fun with this one :)
on 14. August 2026, 20:34 by RedBarchetta
That was fun! A great fresh take on the Skyscraper rule mixed with yin yang. Superb, thanks!
on 14. August 2026, 19:47 by emoney1374
Great puzzle! Nice flow!!
on 14. August 2026, 19:41 by yttrio
Simple concept + great execution = excellent puzzle!
on 14. August 2026, 18:10 by Myxo
Lovely!
on 14. August 2026, 17:13 by Calvinball
Great puzzle, fun logic and even made me laugh a few times.
