Module 6 · Solving problems · Lesson 3 of 5

Breaking a complex problem down

Split it into parts, find the constraints, and simplify where you can.

8 min read · Free — no account needed to read

The idea

Big problems feel overwhelming because the mind tries to hold them all at once. Breaking a problem down means splitting it into parts small enough to think about one at a time: what you need to know, decide and do, and in what order.

Constraints are the fixed edges of the problem: the budget, the deadline, the rules, your available hours, other people’s needs. Naming them early is useful rather than discouraging. Constraints narrow the options, which often makes solutions easier to see.

Simplifying is part of the skill. Ask which parts of the problem matter most, and whether some can be left unsolved, solved roughly, or removed entirely. A complicated plan that solves every part rarely survives contact with a real week; a simpler one that solves the main part often does.

Why it matters

A problem broken into pieces becomes a list of things you can start. A problem kept whole tends to be postponed, because there is never a moment to tackle all of it at once.

See it happen

Wen needs to plan her wedding in six months with a small budget. Every time she thinks about it, she feels overwhelmed and closes the planning document.

The first read

There is so much to do that she feels she needs a free weekend to sit down and sort it all out properly.

With this idea

She lists the constraints — the budget, the date, forty guests — and splits the rest into parts: venue, food, clothes, invitations. She decides the venue first because everything else depends on it, and simplifies food to one family-run caterer.

What changed

She named the constraints, split the problem into parts, and simplified where she could.

Easy to get wrong

• Breaking a problem into so many parts that the list itself becomes overwhelming. Group the parts into a handful.
• Treating every constraint as fixed. Some can be negotiated — check before you plan around them.

What this rests on

Practical wisdom. A widely used way of working. Useful to try — not a scientific law.

• George Pólya — How to Solve It (1945) — A mathematician’s method for problem solving: understand the problem, make a plan, carry it out, look back — useful far beyond maths.

Try it: Parts, edges, simplest version

1. Write a problem that feels too big.
2. List its main parts — no more than five or six.
3. List the constraints you have to work within.
4. Write the simplest version of a solution that would handle the most important part.

Reflect

• Which problem have you been postponing because it feels too big to start?
• Where could a simpler solution be good enough?

Use it in the coming days

Break one big problem into parts this week, and put the first part on your schedule.

Where to do it: My Goals

The parts of a big problem fit naturally as steps under one goal.