This page is part of a web-site devoted to the study of qualitative thinking, with an emphasis on those problems, quite formidable and challenging, called Dragons which can be solved without having to write anything down or perform a calculation. See Dragons for an introduction to Dragons with a physics emphasis, Mostly dragons have answers like yes/no, more/the same/less, left/right, top/bottom, up/down. But also there is a category of such problems called by the philosopher of mathematics Lakatos, Monsters, wherein the problem is to debug what looks like a counter-example to a known solution to a problem.
Other Dragons include Hints and comments from frabjous creatures that may alert you to the fact that your initial solution is false. The design of The Box has been so that many give the canonical wrong answer. Moreover, with conscious discussion with a Dragonmaster they mostly become even more convinced that they have come up with the right answer. Your first solution IS a Monster, in the sense of the term introduced by Imre Lakatos.

Dragons now on-line include the following::
Milko aka The Milko Bottle Problem
The Ilya Revel
Inducia Capillaria I a Lakatosian Monster
Inducia Capillaria II a Mercuric Lakatosian Monster
The Coin Problem
YoYo -- or more strictly YOYO in Upper Case, yoyo in lower case
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Executive Toy -- A Challenge in Metacognition
The BumbleBee Paradox: Why It Can't Fly But Does
The Satellite Paradox: Negative Mass in Low Earth Orbit
Executive Toy -- A Challenge in Metacognition
Cyber -- a 3D Perceptual Dragon
Ayelet's Challenge -- a mathematical puzzle
Sir Arthur Eddington's Cricket Puzzle -- For Cricket Fans only