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Curious Cheetah

Rain Clouds

Background

Arguably a variant of Battleships, a significant difference is that solvers are not told how many clouds there are.
This puzzle appears in "Challenge Your Brain Math & Logic Puzzles" (Dave Tuller & Michael Rios, Puzzle Wright Press).

Puzzle and Goal

An unsolved puzzle consists of a rectangular grid with numbered clues at the end of each rank.
The goal is to color rectangular regions (cloud) to satisfy the clues.

Rules

The solved grid must satisfy the following conditions:

Other Names

Regenwolken

Playable Online