Working Backwards: One Trick That Solves Half the Notebook
Start at the finish and ask what must have happened just before. It sounds too simple to help. It cracks at least five of our puzzles.
When you are stuck on a puzzle, the natural thing is to stare at where you are and try moves. There is another way in, and it is often quicker: stare at where you want to end up, and ask what the position must have looked like one step earlier.
Mathematicians have recommended this for a very long time. It works on a surprising number of the puzzles on GridPencil, and the best way to learn it is to watch it work.
Ice Slide: the flag tells you how to arrive
In Ice Slide you glide until something stops you, and you must stop exactly on the flag. Sliding forwards from the start, you have four choices at every step and most of them lead nowhere.
Now look at the flag instead. To stop on it, there must be a rock or an edge immediately beyond it. Check its four sides. Perhaps there is a rock directly above. Then the last slide has to be upward, along that column. That one observation removes three quarters of the puzzle.
Ask again. Where could you be standing, in that column, below the flag? Only somewhere you can actually stop: beside a rock or against an edge. Usually there are one or two such squares. Pick one and repeat the question. Three or four steps back, you will find a square you already know how to reach.
Tower of Hanoi: the big disc sets the agenda
In Tower of Hanoi the finish is a full stack on the right-hand peg. What has to be true just before the largest disc lands there? The right peg must be empty, and the largest disc must be free, which means every other disc is piled on the middle peg.
So the real first job is not "move the big disc". It is "move everything else to the middle". And that is the same puzzle with one disc fewer. Ask the question again about the second-largest disc, and again, until the answer is a single move. The whole solution unrolls from the end.
Two Jugs: decide what the last pour looks like
Take the classic Two Jugs problem: a three and a five, and you want four. Four can only sit in the five-litre jug. How could that jug come to hold four? One way: it was full, and you poured exactly one litre out of it. You can pour out exactly one litre if the small jug has room for exactly one, which means it already holds two.
So the question becomes "how do I get two litres into the three-litre jug?" And that is easy: fill the five, pour into the three, and two are left over. Empty the three and move the two across.
Read forwards, the six steps look like a trick someone pulled out of the air. Read backwards, each one was forced.
River Crossing: the last trip is the goat
In River Crossing, think about the final crossing. The farmer arrives with the last passenger. Before that trip, two passengers were waiting unguarded on the far bank. The only pair that can be left alone is the wolf and the cabbage. So the last passenger over is the goat.
We already know the goat is also the first one over, because nothing else can leave safely. A passenger that crosses first and last must have come back in between. There is the famous twist, found without any trial and error.
Peg Solitaire: picture the ending
Peg Solitaire is too big to reverse completely in your head, but the idea still helps. The perfect finish is one peg in the centre. The move before that was a jump into the centre, so there were two pegs in a line next to it. Before that, three pegs in some small cluster near the middle.
This tells you what the endgame needs: the last few pegs close together, near the centre. A peg stranded in a far arm of the cross cannot be part of that picture. It is the reason for the old advice to clear the arms early.
When it does not work
Working backwards needs a clear, single target. It is no use in Colour Flood, where the end position tells you nothing about the route. For puzzles like that you want its sibling: looking two moves ahead.
For everything else, try it the next time you are stuck. Among all the habits that HTML5 games like these can teach, it is the one most likely to be useful somewhere else, on a puzzle or off one.