Case: Hideout

Obscured skyscrapers

If we have determined that the minimum number of guaranteed peaks in a half-lane satisfies the clue, then we can deduce that some intermediate cells must be obscured.


3		4			6


3		4	*123*	*123*	6


3		4	123	123	6	5

During peak descent we find cells that are guaranteed to be peaks. Here, we have 3 guaranteed peaks – the solved cells containing the $4$ and $6$ skyscrapers, as well as the unsolved head cell.


3		4			6

These 3 cells are guaranteed to be visible.

This means we’re already guaranteed to satisfy the clue. Which means we can’t then have another peak between the $4$ and $6$ – since then we’d have not 3, but 4 skyscrapers visible.


3		4	5		6

If we had another peak ( $5$ ) in between the $4$ and $6$ , we’d have 4 cells guaranteed to be visible, contradicting the $3$ -clue.

This means those intermediate cells must be obscured, i.e. shorter than $4$ .


3		4	*123*	*123*	6

$\{123\}$ are the available skyscrapers shorter than $4$ .

In this situation, this also lets us pinpoint the $5$ . It can’t go in the head cell, so it must be in the tail cell.


3		4	123	123	6	5