Sunday, 14 August 2022

Freddie Hand

Firstly, congratulations to @Vornicus @Oripy @Yosh @Rosa @jatloe12345 @Nona @J0llywalrus @Ocean/Lightning/Thunder @msl001 who successfully guessed today's puzzle to be a Nurikabe (Skyscrapers)! Well, not the skyscrapers part, but the otters are still willing to oblige. Here is their representative: 🦦

Today's puzzle may have a fairly ordinary shape, but its ruleset is a rather funky one. And who needs Strange-shaped Sunday when we have Euclidean Geometry Sunday?

ABCD is a rectangle, P is the midpoint of AB, and Q is the point on PD such that CQ is perpendicular to PD. Prove that the triangle BQC is isosceles. (from BMO1 2003/4) (image attached)

Rules: Shade some cells so that all shaded cells form one orthogonally connected area. No 2x2 region may be entirely shaded. Clues cannot be shaded, and every orthogonally connected area of unshaded cells contains exactly one clue, the value of which represents the size of the area. A ? can represent any positive integer.

Variant: A clue outside the grid indicates the number of maximal groups of consecutive shaded cells that are visible from the direction of the clue. Groups are obstructed by other groups of the same, or greater, size.

Alternatively, a clue outside the grid indicates how many maximal groups of consecutive shaded cells in the corresponding row or column are longer than all others before them in the same row or column from the direction of the clue.

An extra image is attached to illustrate a few examples of how the skyscrapers clues work.

Example (Penpa+): https://tinyurl.com/2p3gwtne

For a Speedy Sloth 🦥 solve in 4:00 or less!
For a Quick Crab 🦀 solve in 8:30 or less!
And all who finish get a Nifty Neddicky 🐦

Puzzle (Penpa+): https://tinyurl.com/2oho2hz8