The 2-Minute Technique That Saved Me When I Had Zero Idea How to Solve an Exam Question

I was sitting in my math final, staring at question 7.

“A train leaves Station A at 3:47 PM traveling 85 km/h. Another train leaves Station B at 4:12 PM traveling 92 km/h. If the stations are 437 km apart, when will they meet?”

My mind went completely blank.

We’d practiced distance-speed-time problems, sure. But this? Two trains starting at different times, moving toward each other? I’d never seen this exact setup before. Nothing in my notes matched this pattern.

I could feel panic rising. This question was worth 15% of the entire test. I couldn’t just skip it.

Think. There has to be a way to start.

That’s when I remembered something my older brother told me after he bombed his physics test: “When you have no idea what to do, just write down what you DO know.”

It sounded too simple to actually work. But I was desperate.

So I started writing.

What Happened When I Stopped Trying to “Know” the Answer

Here’s what I wrote on my exam paper, exactly as it appeared:

What I know for certain:

• Two trains
• Moving toward each other
• Train 1: 85 km/h
• Train 2: 92 km/h
• Distance between them: 437 km

I stared at that list. Still had no idea how to solve it.

But then I asked myself: “Okay, what MUST be true if those facts are true?”

And suddenly, something clicked.

If they’re moving toward each other, the gap between them has to be closing.

I wrote that down: “Gap between trains is closing.”

Then I asked: “How FAST is the gap closing?”

And that’s when I saw it. Train 1 is eating up 85 km of the gap every hour. Train 2 is eating up 92 km every hour. Together, they’re closing the gap at 85 + 92 = 177 km per hour.

Gap closes at: 177 km/hour

Now the solution appeared: If the gap is 437 km and it’s closing at 177 km/hour, then 437 ÷ 177 = 2.47 hours until they meet.

I went from complete paralysis to solving a problem I’d never seen before. Not by recognizing a pattern or remembering a formula, but by building the solution one logical step at a time from basic facts.

That’s first principles thinking. And it saved my grade that day.

Why Being Stuck Isn’t About Being Stupid

Here’s what I realized: I wasn’t stuck because I was bad at math. I was stuck because I was trying to RECOGNIZE the problem instead of REASON through it.

Most of the time in school, you solve problems by pattern matching:

• “Oh, this looks like that problem from homework”
• “This is the quadratic formula situation”
• “I remember doing something like this before”

Pattern recognition is fast and works great when you’ve seen similar problems. But when you face something new, your pattern-matching breaks down. You search your memory for a match, find nothing, and panic.

That’s what happened to me with the train problem. My brain kept searching: “Where have I seen this before? What’s the formula? What’s the pattern?”

Nothing matched. So I felt stuck.

But here’s the thing: Just because you don’t RECOGNIZE a solution doesn’t mean you can’t BUILD one.

The Technique: Building Solutions From Scratch

First principles thinking is simple: When you’re stuck, stop trying to remember and start reasoning.

Here’s exactly how it works:

Step 1: Write down what you know for absolutely certain

Not what you think might be relevant. Not what you vaguely remember. Just facts you’re 100% sure about.

For the train problem:

• Two trains exist
• They’re moving toward each other
• Specific speeds for each
• Specific distance between stations

Step 2: Ask “What must be true if THOSE facts are true?”

This is where reasoning starts. Given what you know for certain, what logically follows?

Two things moving toward each other? The distance between them must be getting smaller.

Step 3: Ask “What follows from THAT?”

Keep building. Each answer becomes the foundation for the next question.

Gap is getting smaller → How fast? → Each train’s speed → They add together → 177 km/hour

Step 4: Continue until you reach the solution

Gap closes at 177 km/hour → Starting gap is 437 km → Time = 437 ÷ 177 hours

Each step is tiny. Each step is certain. And together, they build a complete solution.

Why This Actually Works

Think about what just happened with the train problem.

I didn’t know the “formula” for two trains meeting. I didn’t have a memorized pattern. But I DID know some basic truths:

• Moving toward each other = gap closing
• Speed = distance per time
• Combined motion = combined speeds

Those basic truths were enough. I built the solution from pieces I already had.

That’s the power of first principles: You always have SOMETHING you know. Even when you feel completely stuck, there are basic facts you’re certain about. And those facts, reasoned through logically, can lead you to answers you didn’t know you could reach.

Real Example: Chemistry Confusion

Let me show you how this works in a different subject.

My chemistry teacher asked: “Why does sodium react violently with water?”

I panicked. We’d learned about reactions, sure, but this specific combination? No memory of covering it.

What I did:

What I know for certain:

• Sodium is an element
• Water is H₂O
• When they touch, there’s an explosion
• We learned atoms react to become stable

What follows from that? If atoms react to become stable, then stable atoms DON’T react. (Logical step)

What follows from THAT? Noble gases don’t react with anything. So noble gases must be “stable.” (Evidence + reasoning)

What follows from THAT?
What makes noble gases stable? They have full outer electron shells. (Fact I remembered)

What follows from THAT? So atoms try to get full outer shells. (Logical conclusion)

What follows from THAT? Sodium has 11 electrons: 2, 8, 1. The outer shell has just 1 electron. (Fact from periodic table)

What follows from THAT? Easier to lose 1 electron than gain 7. So sodium wants to give away that electron. (Logic)

What follows from THAT? Water can take electrons (hydrogen wants more). So when sodium meets water, electron transfers. (Connection)

Final step: Electron transfer releases energy. Lots of transfers at once = explosion. (Solution)

I went from “I have no idea” to understanding the complete mechanism, just by asking “what follows from that?” over and over.

The Emergency Exam Protocol

Next time you’re stuck on a test question, try this:

1. Stop and breathe (5 seconds) Don’t panic-skip. Don’t guess randomly. Just take one breath.

2. Write down certainties (30 seconds) “What do I know for absolutely sure about this problem?” Even if it seems too basic, write it down.

3. Ask what follows (1 minute)
“If THAT is true, what else must be true?” “What’s the simplest logical next step?”

4. Build up one step at a time Keep asking “what follows?” until you either:

• Reach a solution, or
• Get partial credit for logical reasoning

Even if you don’t get the complete answer, you’ve:

• Broken the paralysis (you’re working, not frozen)
• Shown logical thinking (teachers give partial credit for this)
• Possibly stumbled onto the right approach

When to Use This vs. Finding Patterns

I use two different techniques depending on what I’m facing:

Finding patterns (connecting new stuff to what I already know): When something REMINDS me of something familiar.

• Chemistry bonding looks like historical alliances? Use the alliance logic I already know
• This math problem feels like that physics problem? Try the same approach
• Works great when I can spot the connection

Breaking down to basics: When NOTHING looks familiar or I can’t find a pattern that fits.

• Start with simple facts
• Build up step by step
• Takes a bit longer, but works every time

Here’s how they work together:

Let’s say I’m stuck on a physics problem about momentum.

First try: Does this remind me of anything? (Looking for patterns)

• Hmm, momentum is like… carrying a heavy box? No, that’s not quite right.
• Maybe like a moving train? Feels forced.
• Pattern finding isn’t working.

Switch to breaking it down: What do I know for sure?

• Momentum means “how hard it is to stop something”
• Heavier things are harder to stop (fact)
• Faster things are harder to stop (fact)
• So momentum must involve BOTH weight and speed (logical step)
• Momentum = mass × velocity (just built the formula from basics!)

Now patterns work again:

• Oh! This IS like that train problem – combining two things (mass and speed) instead of one
• Now I can use train logic on momentum problems

See how they help each other? Try patterns first (faster). If it feels wrong, break it down. Once you understand the basics, patterns start appearing.

What This Actually Teaches You

Here’s what makes this different from memorizing more formulas or test tricks:

This is real problem-solving.

When you face something new – in college, at a job, in life – you won’t have someone’s formula to apply. You’ll need to reason from what you DO know to what you need to figure out.

That’s what this technique builds:

• Comfort with being stuck (it’s not “I’m dumb,” it’s “I need to reason through this”)
• Logical thinking under pressure (exams, meetings, emergencies)
• Confidence that you can figure out new situations
• Actual thinking, not just pattern matching

My parents saw my grades improve. But what they really noticed was that I stopped saying “I can’t do this” and started saying “Let me think through this.”

That mindset shift? That’s the real value.

Try This Tonight

Pick one confusing concept from any of your classes. Something that didn’t make sense in the textbook or lecture.

Instead of re-reading it or asking someone to explain it, try this:

1. Write down the most basic fact you know about this topic
2. Ask: “What must be true if THAT is true?”
3. Write that conclusion
4. Ask: “What follows from THAT?”
5. Keep going

You might surprise yourself. Even if you don’t reach complete understanding, you’ll have reasoned further than you thought possible.

What Else Is In My First Principles Guide

This blog gives you the emergency method – what to do when you’re stuck on a test.

But in my complete First Principles guide, I go way deeper:

I break down actual school subjects step-by-step:

• How to analyze Lord of the Flies using first principles (start with “why would anyone act this way?” and build up)
• Chemistry reactions explained from scratch (I show you exactly how to reason through sodium + water, acid + base, and more)
• Math word problems broken down completely (trains, mixing problems, even those confusing rate problems)
• Physics concepts built from basics (momentum, forces, energy – all from simple facts)

I show you when to break things down vs. when to find patterns:

• Real examples where I tried patterns first, they didn’t work, so I switched
• Problems where breaking it down first made the pattern obvious
• How to tell which method fits what you’re facing

You get the actual AI prompt I use:

• Copy and paste it into ChatGPT or Claude when you’re stuck
• It walks you through the “what do you know?” questions
• Guides your reasoning without giving you the answer
• Like having a tutor who helps you think instead of doing it for you
• (It speeds up learning without cheating, but honestly, it feels like cheating)

Plus examples from every subject:

• History: Why did the French Revolution happen? (Build from basic human needs up)
• English: How to find themes in any book (start with “what happens?” and reason to “what does it mean?”)
• Science: Biology, chemistry, physics – I show you the basic facts for each and how to build understanding
• Math: Algebra, geometry, even calculus – broken down to kindergarten level then built back up

The difference between this blog and the guide:

This blog teaches you the emergency technique and shows you it works.

The guide gives you the complete breakdown for the subjects you’re actually studying right now. Instead of figuring out “what are the basic facts about chemistry?” on your own, I’ve already done that work and show you exactly where to start for each topic.

Plus you get practice problems, the AI prompt, and real examples of me using this on tests, homework, and even college applications.

Want the full system? Check out the First Principles Thinking guide here:

You’ll never feel completely stuck again – because you’ll always know how to start from what you DO know and build to what you need.

Ps: When you’re interested in more of these techniques, you can check out this page where we collect all Meta Learning Techniques