Hanoi: 31 moves. 15 puzzle: 72 moves. Leaping frogs: 15 moves. Lights out: 15 moves. Peg solitaire: 13 moves. This took 2 hours. 1 hour 45 minutes for peg solitaire, 15 for everything else. These are the theoretical best possible speedruns.
websites i got the solves from: https://www.mathsisfun.com/games/triangle-peg-solitaire/index.html https://www.jaapsch.net/puzzles/lights.htm#desc https://www.jaapsch.net/puzzles/javascript/hanoij.htm https://www.jaapsch.net/puzzles/javascript/lightjcl.htm https://www.jaapsch.net/puzzles/javascript/fifteenj.htm