Inventive Working Backwards Technique for Problem solving

Sometimes you need to start your problem solving analysis from the end

Most of us start problem solving from the beginning, and work our way to the end. But, working backwards technique often proves to be the only way to solve.

When we face a problem, we tend start the process with our first decision regarding the first barrier we see in front of us, then take the second decision and the next and thus move towards the solution step by step.

If we are fortunate, we reach the solution somehow. This is start-to-end step by step problem solving in a linear forward direction. This also is the naturally adopted direction of problem solving for most of us.

Many a time though we need to start our analysis from the end event and work backwards to the beginning event.

Case example 1: Journey planning

When my niece told me her important admission test would be held at Kalyani in the morning I sensed a problem. Kalyani is a few hours' drive away from Kolkata by road. Morning time meant we had to start early and be careful in deciding how we traveled. A wrong decision might lead us to failure in reaching at right time.

By the first hand information, it seemed it is faster to reach by train rather than by road. But there may be a number of trains in the morning for Kalyani. Now the decision to be taken is - which train to catch?

• I asked my niece, "What is the time of reporting?" She said, not enthusiastically, "It is 8.45 in the morning. It'd take at least an hour to reach Kalyani station from Bidhannagar (our station). There are buses and other conveyances from the station to the venue of test. It'd take at least 15 minutes more to reach the campus."
• I told her to decide which train to take and its time of arrival at our station.
• Next day when I asked her about the situation, she said a little hesitantly, "I think we should take the 6.15 train." When I asked her how she arrived at the decision, she explained, "I got the times of the morning trains.
• The journey would take about an hour and fifteen minutes. So we would reach Kalyani at about 7.45 safely if we take the 6.15 train."
• "Alternatives?" I pursued. "There are a few other trains around that time, but this looked to me the most suitable." She replied. Then I explained the goodness of Working backwards approach for this decision making problem.

This is a simple problem, but when we face this kind of problem, we always work backward to be absolutely clear about our first decision.

1. End state: To report at the venue by 8.45 am. So we must target to reach the venue by 8.30 am latest. 15 minutes is the buffer time. To be sure of reaching a place or meeting a deadline in our daily life, we always use this buffer time concept.
2. End minus 1 step: To reach the gate of the venue by 8.20 am, as at least 10 minutes may be required to reach the test hall from the gate of the large campus. This is a minor detail and never to be ignored.
3. End minus 2 step: We should keep at least 30 minutes to reach the test campus gate from Kalyani station. Kalyani is not a large city, and transport options may not be many. You need also to account for the time to get down from the train and select and board the conveyance that would take you to the campus gate. Rolling back 30 minutes from 8.20 am, we should then take such a train that would certainly reach Kalyani by 7.50 am.
4. End minus 3 step: With this theoretically safe time of reaching Kalyani station, we must add some buffer as the train might delay on the way. It might also arrive at Bidhannagar, our starting station later than scheduled time. These delays happen. So, I concluded, It is safer to choose an earlier train. The choice of 6.15 train seemed to be ok, but we chose the 6.10 train to keep the buffer for canceled or delayed trains.
5. Not surprisingly, our train arrived a bit late. Getting a conveyance from Kalyani station to the test venue campus was a hassle, and we had to take a quick last minute decision. We reached finally by 8.35 - safe and dry.
6. End minus 4 step: With (End minus 3 step) decision taken, journey planning was not over though. I asked her, "To catch the train arriving at 6.10 am, when should we start from home?" That was not complicated, but still it is better to fix this predictable and more certain event also on the event timeline to make the whole time-line transparent and ease up decision making and anxiety during the actual journey.

Practical experience says,

There are always deviations from what you plan and what happens.

Though the instinctive decision of my niece was not much off the mark, when we finished the systematic journey planning process using working backwards approach,

• Our decision became more robust and
• We could see clearly all the events in the whole journey that we would have to go through.

Gains from the experience:

1. This awareness of details is useful for tackling unforeseen situations with more confidence.
2. The entire process increased our confidence in our decisions and resulted in reduced anxiety.

My verification of the effective journey planning method:

For my niece it was her first journey outside Kolkata where she had to take part in decision making. When I discussed this problem with one of my younger but more experienced friends, his time estimates were spot on and coincided with our estimates. Invariably he started from End event - the goal.

My friend remarked casually, "When we started our career we also tried to plan our journey from the starting time, not the ending target time. Now with experience we do backwards journey planning using buffer times automatically."

Experience builds similar kinds of problem solving mechanisms in most people but with varying degrees of intensity.

Case example 2: Thinking backwards to locate misplaced or lost items

How I lost the bunch of my house keys:

In Personal life, I resort often to working backwards to remember where and when I misplaced or lost an important item. Especially, I remember a day when I was moving through a series of hectic actions, often going out of my home. Whenever I go out I lock the gate and take the key with me.

Other members can open the gate in my absence with duplicate keys and when I return I won't have to bother anyone for opening the door. That day when I returned home finally, I found the door open. After entering I reached for my key in my pocket to place it on the key hook by the side of the door, I found I don't have the key. I was deeply shocked.

Losing the bunch of keys outside my home would have serious consequences. I have to change all the keys in the bunch for safety—a very tedious and irritating process.

The mental stress I went through:

With a duplicate bunch of keys, I went out again and slowly retraced my path to a nearby workshop. All the while my eyes were searching on the road surface for a gleam of metal. No trace at all. Even when I reached the last visited workshop, I found it closed and no bunch of keys lying nearby.

The case story ending:

Dejected, I returned. This time after settling down I started thinking.

• Which of the rooms I go to before I left for the first time?
• Moving through my rooms with half expectation, I was more relieved than surprised to find the key bunch lying innocently on a corner of my table.
• While in hurry, I took the bunch but didn't take it with me when I went out. Instead, in between my hectic activities, I put it on the table and forgot all about it.

Working backwards approach is a powerful inventive problem solving technique used in many real life problem solving situations. For planning and execution of large and complex projects with fixed target time point, working backwards is an essentiality.

This is an inventive problem solving technique that most people with experience have used in one point or other in their lives, but always being unaware of the separate well-defined technique they used.

People are unaware problem solvers.

Though we use this technique frequently in real life, we find from the literature available that formalism to this approach was given by the mathematicians. This is not surprising, as effects of problem solving techniques or approaches can be clearly showcased in the more certain and specific world of mathematics.

Can you identify other real life scenarios where working backwards produces much better results?

• Preparing for an exam, preparing for a lecture, organizing for an event where you have fixed amount of preparation time are only some of the real life scenarios where you would automatically use this powerful problem solving approach.

Frequent use of such a basic problem solving technique makes it a part of your reflexive problem solving mechanism, no less.

• More importantly, awareness and clarity of the inventive working backwards system makes you solve problems in which most people become confused and many cannot reach the solution. These are the cases when the inventive technique attains its true potential of INVENTIVENESS.

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Case example 3: Inventive Working Backwards Technique for Problem Solving of Puzzles

Most people with experience are aware of the necessity for working backwards in journey planning. In this area, the role of working backwards technique doesn't bring out its inventive quality.

But, the following puzzle highlights the power and inventiveness of the Working Backwards technique. It serves as an example of a problem that would be impossible to solve without knowing or discovering this method.

The Puzzle that highlights the power and inventiveness of Working backwards technique

The half a poodle riddle

Sonia breeds French poodles as a hobby. She sold half of her puppies and half a puppy from the latest litter to the local pet shop. Next, she sold half of the puppies that were left in the litter and half a puppy to Puppy Palace. She then gave the remaining puppy to her friend Kaveri.

How many puppies did the original litter have? You cannot use Algebra.

Do give it a try to realize the difficulty in deciding how to start.

If you wish, you may go through my article on the riddle:

How Could Sonia Sell Half a Poodle Riddle.

My field test of the puzzle's ease or difficulty in solution

While I and my son along with many others were waiting for the results of the selection for a seat in MSc Zoology in Banaras Hindu University, we got very bored and tired because of the 8 hour plus waiting.

Beside me I found a young aspirant, a girl from West Bengal. To relieve boredom, I asked her, "Would you like solve a cute puzzle?" She agreed, and I described the puzzle to her.

After a few minutes of trying, she gave up.

And a little later I found her sitting somewhere else.

Such is the power (or lack of power) of not being aware of the inventive technique of Working backwards.

Solution hint: With the inability to assume an unknown as X, as you do in basic Algebra, what course of thinking is available to you? What's that thing you know for certain in this riddle?

It simply is: the END result—Sonia had just ONE puppy at the end, which also she gave away as a gift (this last part is a decoy).

Won't you be able to examine what Sonia did before she ended up with just one puppy? That will be your END-1 State.

Go one backwards and you'll get the answer in under only a minute,

• If you discover the inventive technique yourself (which I did after quickly realizing that conventional thinking won't help), or
• What is common with most people, you are not really aware of the inventiveness inherent in the working backwards technique.

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Many Applications of Working Backwards Technique in Real Life Problem Solving

The list is long and can be extended further. It shows how basic this unusual thinking process is. Ponder a moment on each to imagine how the technique may work in the area.

And, who knows, someday you will actually face such a problem and this exposure to get over the hurdles smoothly!

Working backwards in mathematics:

• Mathematicians often use this to crack tough problems. Instead of staring at a complex equation wondering how to begin, they first assume the solution exists. They then ask, "What must be true just before the final step?" and "What must be true before that?" This process of unraveling the logical prerequisites step-by-step backwards from the solution often reveals a clear, elegant path from the problem to the answer that was impossible to see from the start.

Working backwards in puzzle solving:

• Consider a logic puzzle where you must deduce who owns the zebra based on clues. A forward approach might lead to dead ends. An expert solver starts from the end goal: "There must be a complete grid where all clues are satisfied." They then use the most restrictive clue (e.g., "The person in the blue house drinks milk") to anchor one fact and work backwards, asking, "If this is true, what other facts are forced to be true?" This method efficiently narrows down possibilities.

Working backwards in journey planning:

• As detailed in the main article, you start from the non-negotiable arrival time (the goal) and subtract time for each preceding step: parking, walking from the car, traffic, and finally, the time you must leave home. This builds in essential buffer time and creates a robust, stress-free plan, ensuring you are late only if a truly catastrophic event occurs.

Working backwards in conflict management:

• A mediator doesn't just ask two arguing parties what they want. They start by envisioning the ideal end state: a signed agreement where both feel their core interests are addressed. They then work backwards to uncover the underlying needs and fears behind their stated positions. By identifying the compromises and trust-building steps needed to reach that final agreement, they can construct a path forward that feels intentional and possible for everyone.

Working backwards for event management:

• An event planner starts with the event itself: a flawless gala dinner at 8 PM on a specific date. Working backwards, they calculate: food must be served at 8, so cooking must start at 6, so ingredients must be delivered at 3, so the order must be placed a week prior. They also need the venue setup by 5 PM, which requires hired staff to arrive at 1 PM, and invitations must be sent out 6 weeks in advance to ensure good attendance. The entire project plan is built from the deadline.

Working backwards for scheduling exam preparation:

• A student knows their final exam is on December 15th. Their goal is to be thoroughly reviewed by December 12th. Working backwards, they block out the last three days for practice tests. This means all new material must be learned by December 9th. They then break the syllabus into weekly chunks, working backwards from the 9th to the start of the semester, creating a realistic and manageable study schedule that avoids last-minute cramming.

Working backwards to catch a murderer in detective work:

• This is the classic detective trope. The detective starts with the end result: the victim and the crime scene. Every clue—the murder weapon, the time of death, the motive—is a piece of evidence that points to a sequence of events that must have happened before the murder. The detective reconstructs the victim's last hours, the perpetrator's actions, and the lead-up to the crime, effectively making a movie of the past that ends with the scene in front of them.

Working backwards in psychiatric treatment of a trauma patient:

• A therapist helps a patient overcome a debilitating phobia. They start with the goal: the patient calmly encountering the feared object. Right before that, the patient must be able to be in the same room with it. Before that, they must be able to visualize a picture of it. Before that, they must be able to discuss it without anxiety. The therapist designs a treatment plan (exposure therapy) that follows this backward sequence, building confidence step by step.

Working backwards in reverse engineering:

• A company wants to build a competitor for a popular gadget. They acquire the gadget, disassemble it, and analyze its components and how they fit together (the end state). By understanding the finished product intimately, they can deduce the manufacturing processes, design choices, and software algorithms that must have been used to create it, allowing them to replicate or improve upon the design.

Working backwards in project management:

• This is formalized as "Backward Planning" or "Goal-Based Planning." The project manager defines the final deliverable and its due date. The team then lists all final tasks that must be completed right before launch (e.g., final testing, packaging). They continue asking "What must be done immediately before this?" until they reach the project's starting point. This ensures every single task is directly tied to achieving the final goal on time.

Working backwards for product launch:

• A company aims to launch a new app on January 1st. Working backwards, they know they need a marketing campaign to start December 1st. This requires finished promotional materials by November 20th, which need the final app design locked in by November 1st. This requires beta testing in October, which requires a working prototype in September, and so on. This creates an unbreakable time-line for the entire team.

Working Backwards in Financial Planning:

• Someone dreams of retiring with a $1 million portfolio in 20 years (the goal). A financial planner works backwards: to have $1M in 20 years, given an estimated rate of return, you must invest $X per month starting today. This backward calculation transforms a vague dream into a concrete, actionable monthly savings goal.

Working Backwards in Software Development:

• Modern methodologies like Agile use this. Developers first write a test that defines what a perfect piece of code should do (the end goal). This test will fail initially. They then write the simplest code possible to make that test pass, effectively building the solution backwards from the defined successful outcome. This ensures the code is efficient and meets exact requirements.

Working Backwards in Supply Chain Management:

• A retailer needs 10,000 units of a toy on shelves by November 15th for the holidays. Working backwards, shipping from the port takes 2 weeks, so the ship must arrive November 1st. Ocean freight takes 4 weeks, so the container must be loaded in China on October 1st. Manufacturing takes 3 weeks, so the order must be placed with the factory by September 10th. This prevents stock-outs.

Working Backwards in Crisis Management:

• During an oil spill, the goal is to be "fully contained and cleaned up." Command centers work backwards from this goal: to clean up, the oil must be contained with booms. To deploy booms, we need ships and good weather forecasts. To get ships, we need to activate emergency contracts. This backward planning prioritizes immediate actions that will inevitably lead to the final resolution.

Working Backwards in Career Planning:

• A student dreams of becoming a lead engineer at a tech firm. They research and find that most leads have 10 years of experience and an advanced degree. Working backwards, they plan: "To have 10 years of experience by 40, I need to start my career at 30. To start at 30, I need my Master's degree by 29, which means I must apply to programs at 27." This turns a lifelong ambition into a decadal roadmap.

Working Backwards in Marketing Campaigns:

• The goal is a massive sales spike on Black Friday. The campaign must peak on that day. Working backwards, PR pushes happen the week before, social media ads ramp up two weeks prior, influencer content drops three weeks out, and the entire campaign strategy is built months in advance, all timed to perfectly converge on the target date for maximum impact.

Working Backwards in Urban Planning:

• A city wants a new downtown park completed by 2030. Planners work backwards: construction will take 2 years, so bidding must start in 2028. Design and approval will take 3 years, so the design committee must be formed in 2025. Community consultation and funding votes must happen in 2024. This backwards time-line ensures the project stays on track for decades.

Working Backwards in Environmental Policy Development:

• The goal is to reduce carbon emissions 50% by 2040. Policymakers work backwards: this requires widespread electric vehicle adoption by 2035, which requires charging infrastructure by 2030, which requires grants and regulations to be passed by 2025. This identifies the critical, immediate legislation needed to make a distant goal achievable.

Working Backwards in Historical Research:

• A historian studies a revolution. They start with the known outcome: a new government was formed on a specific date. They then work backwards to ask: "What battle immediately preceded this?" "What political declaration preceded that?" "What economic crisis sparked the unrest?" This helps identify the true causal chain, separating myth from fact.

Working Backwards in Recipe Development:

• A chef wants a new dessert with a crisp caramel top. The end state is the finished dish. They reason backwards: to get a crisp top, they must use a blowtorch or broiler at the last second. Before that, the dessert must be chilled, so it must be assembled hours before. Before that, the base (e.g., a mousse) must be set. The entire recipe is constructed from the final desired sensory experience.

Working Backwards in Real Estate Development:

• A developer wants a building fully leased by Q4 2026. Tenants need 3 months to build out space, so construction must be complete by Q2 2026. Construction will take 18 months, so they must break ground by Q4 2024. Permits take 12 months, so they must acquire the land and apply by Q4 2023. This backwards schedule drives all investment and planning decisions.

Working Backwards in Business Strategy:

• A startup aims for an IPO in 7 years. To IPO, they need to show 5 years of profitable growth. To be profitable, they need to achieve a certain market share by Year 5. To get that market share, they need a specific product launch by Year 3. This backwards chain defines their entire strategic roadmap from day one.

Working Backwards in Artistic Creation:

• A sculptor envisions the final form of their statue trapped within a block of marble. They don't just start chipping away randomly. They work backwards from that mental image, identifying which pieces of stone must be removed last to reveal delicate features, and which can be removed first to define the rough shape. Every strike is planned from the finished vision backwards.

Working Backwards in Legislative Processes:

• Advocates who want a law passed by a certain date work backwards from the governor's signature. This requires a vote, which requires a committee hearing, which requires a bill draft, which requires building a coalition of supporters. This backwards time-line creates a critical path for activism and lobbying efforts.

Working Backwards in Educational Curriculum Design:

• Educators start with the "enduring understanding" they want students to have after a course (e.g., "Understand the causes of WWII"). They then work backwards to design the final exam that tests this. Then, they create the lessons and activities that provide the knowledge and skills needed to pass that exam, ensuring every class session is purposefully aligned with the final goal.

Working Backwards in Diplomatic Negotiations:

• Before a summit, diplomats envision the ideal joint statement. They then work backwards to identify the key compromises on specific issues (Trade, Security) that must be achieved to make that statement possible. This helps them prioritize their negotiating points and understand the give-and-take required for a successful outcome.

Working Backwards in Theater Production:

• Opening night is immovable. The director works backwards from it: final dress rehearsals must happen the week before, technical rehearsals with lights and sound the week before that, blocking must be finished a month prior, and casting must be completed three months before opening. This reverse schedule is the backbone of any production.

Working Backwards in Sports Coaching:

• A coach aims to peak their team's performance for the championship game. They work backwards from that date. The week before is for light practice and strategy. The month before is for intense conditioning and scrimmages. The months before that are for building fundamental skills. This periodization ensures athletes are at their best when it matters most.

Working Backwards in Customer Service:

• A support agent's goal is a resolved, satisfied customer. To get there, the customer must confirm their problem is fixed. Before that, the agent must implement a solution. Before that, they must diagnose the problem. Before that, they must understand the customer's description. This backwards logic is the foundation of effective troubleshooting flows.

Working Backwards in Novel Writing:

• Many authors start by outlining the ending—the climax and resolution. They then work backwards, asking, "What event must happen to make this ending possible?" and "What conflict must arise to make that event happen?" This ensures a tight, cohesive plot where every chapter logically propels the story toward its predetermined conclusion.

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The True Inventive Power of Working Backwards Technique: Creation and Discovery

While the technique is powerful for planning and analysis, its true inventiveness shines when used not just to plan or deduce, but to create and discover what is not yet known. This is where working backwards moves from a management tool to an engine of innovation.

Working Backwards in Scientific Discovery:

• A scientist doesn't just run experiments randomly. They start with a desired revolutionary outcome: "A single vaccine effective against all influenza strains." Working backwards from this "inventive goal," they ask: "What antigen would provoke that universal immune response?" "What viral structure must we target?" "What experiment would prove this target is viable?" This backward chain from the ambitious goal defines a radically new, high-impact research pathway that forward-looking, incremental thinking might never conceive.

Working Backwards in Product Invention:

• The inventor of the microwave oven did not start by tinkering with magnets. They started with the inventive end-state: "Food must be cooked instantly from the inside with invisible waves." Working backwards, they asked: "What energy source can penetrate food?" "What device generates this energy?" "How can it be contained safely?" This backward reasoning from a magical outcome forced the invention of entirely new components and principles, creating a category that never existed before.

Working Backwards in Business Model Innovation:

• Companies like Amazon use this inventively. For Amazon Web Services (AWS), the goal wasn't to sell server space. The inventive goal was: "Make it so any developer in the world can build a scalable application in minutes, with no capital investment." Working backwards from this vision forced the invention of a entirely new paradigm: on-demand, pay-as-you-go cloud computing infrastructure, which meant inventing the technical, operational, and business models to make it possible.

Working Backwards in Narrative Art (Beyond Plotting):

• While many authors plot backwards, the truly inventive use is in thematic creation. A writer starts with the emotional or philosophical impact they want the reader to feel at the end: "A profound sense of melancholy hope." Working backwards, they ask: "What final image or character action would evoke this?" "What crisis must precede that to make it earned?" "What beliefs must the character hold at the start for this transformation to be monumental?" The entire story is engineered backwards to manufacture a specific, powerful invention in the reader's mind.

Working Backwards in Ethical Framework Design:

• An organization wants to build a truly ethical AI. Instead of adding rules as problems arise (forward-thinking), they work backwards from the inventive goal: "An AI that is provably fair and unbiased." They ask: "What logging and accountability structures must be in place to prove fairness?" "What design principles, enforced from the first line of code, make bias impossible?" "What does a 'fairness test' look like before any data is collected?" This backward invention of the requirement forces the creation of new tools, standards, and methodologies that redefine the field.

The Key Differentiator: In these inventive applications, the end goal is not a fixed point on a time-line to be met, but a radical new reality to be architected.
The working backwards process becomes a method for forcing the necessary breakthroughs and innovations required to make that unprecedented reality possible. It is the technique for building the bridge from a "what if" to a "how to."

Read on other intellect empowering problem solving techniques here.

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