The 15-puzzle is a classic logic challenge: slide numbered tiles around one empty space until the numbers are in order, from 1 to 15. Every board in this game is generated from legal moves, so every puzzle is solvable.
Color Flood is a relaxing color-matching puzzle. Start in the top-left corner and grow one connected region until it covers the 10×10 board. Each new color absorbs neighboring cells of that color, making your region larger with every move.
Peg Solitaire is a classic single-player logic puzzle. Start with 32 pegs and one empty hole in the center. Jump one peg over another into an empty hole; the jumped peg is removed.