Imagine you’re standing at the entrance of a vast, intricate maze. There are dozens of paths branching out, each leading to more choices, more dead ends. The sheer number of possibilities can feel overwhelming. Now, what if you could magically transport yourself to the finish line and simply trace the one correct path back to the start?
That, in essence, is the problem-solving superpower known as “Working Backwards.” It’s a counter-intuitive yet incredibly effective strategy used by mathematicians, detectives, and expert puzzle solvers.
Welcome to Sequentia, where today we’re adding this powerful technique to your mental toolkit!
What is Working Backwards?
Most of us approach problems linearly. We start at the beginning (the known information) and try to forge a path forward to the end (the unknown solution). But when a problem has too many starting paths or variables, this can lead to a lot of wasted effort.
Working backwards flips the script. You start with the known end result or goal, and then, step-by-step, you deduce the immediately preceding step. You ask, “What had to happen right before this?” and then, “What had to happen right before that?” You continue this process until you arrive back at the beginning.
Why is This Strategy So Effective?
- It Simplifies the Problem: The end of a problem often has fewer variables than the beginning. The goal is a single, known point. By starting there, you are working with a concrete fact rather than a cloud of possibilities.
- It Reduces Branching Paths: Moving forward from the start often presents a “tree” of branching choices. Moving backward from the end frequently follows a more singular, direct path, making it much easier to navigate.
- It Provides a Clear Target: Every step you take backward has a clear and immediate goal: to figure out the previous step. This focused approach prevents you from getting lost in speculative or irrelevant paths.
Working Backwards in Puzzles
This isn’t just an abstract concept; it’s a practical tool for many of the puzzles we love:
- Mazes: The classic example! Instead of trying every path from the start, begin at the “Finish” and trace the correct path back to the “Start.” There is only one way out.
- Number Sequences: Sometimes, the rule in a sequence is clearest at the end. For a sequence like 3, 7, 15, 31, ?, instead of figuring out how 3 becomes 7, try working backward. How did 31 result from 15? (Multiply by 2, plus 1). Does that rule work for 15 and 7? (7 x 2 + 1 = 15). Yes! The pattern is confirmed.
- Logic Puzzles: If you know the final outcome (e.g., “The person who owns the cat lives in the blue house”), you can use that solid fact to work backward and eliminate other possibilities for the cat owner and the blue house.
Even in real life, this works wonders. Planning a big event or a trip? You start with the event date (the end goal) and work backward to set deadlines for booking venues, sending invitations, and arranging travel.
So, the next time you feel stuck on a complex problem, take a deep breath and ask yourself: “Can I start from the end?” You might just find that the path forward becomes clear by looking backward.
Have you ever used this strategy to crack a tough puzzle? Share your stories in the comments!