Fix it
Find the dead bulb in five tests, not thirty-two.
Try it
The whole string is dark: one bulb is broken. Drag across some bulbs to pick a stretch, then test it.
- Tests
- 0
- Still suspect
- 32
Now a real one: the lamp will not turn on
The lamp by the sofa worked last night. Tonight the switch clicks and nothing lights. Pick your next check. Each one takes a little time; the minutes are rough guesses for the game.
0 min spent
What do you check first?
What just happened
Split it in half
Each test splits the bulbs in two: the stretch you test and the rest. The break is on one side, so the other side is cleared. Test half of what is left and every test clears half: 32, 16, 8, 4, 2, 1. That is 5 tests, every time. One bulb at a time clears one bulb per test: up to 31 tests, 16.5 on average. The halving move has a name: a binary search.
31tests at most, one at a time
5tests at most, halving
32, 16, 8, 4, 2, 1
Why the halving count barely moves
Run it backwards. One test can settle 2 bulbs. Each extra test doubles what you can search: 2, 4, 8, 16, 32. So 32 bulbs take 5 tests, and 64 take only 6.
Keep doubling and it gets big fast. Twenty doublings make 1,048,576, so twenty halving tests can find one bad item among a million. One at a time, the same search could take 999,999.
Simple things first, one change at a time
In the lamp game the cheap checks come first: the plug, the switch, the rest of the room. Each takes a minute and rules out a lot. Then change one thing at a time. If you swap the bulb and move the lamp together and it lights, you cannot say which change did it, and next time you start from zero.
Define it before you fix it
Say what is wrong in one plain sentence: what, where, since when. “The dishwasher is broken” is a start. “Water stays in the bottom after every cycle since Sunday” tells you where to look. Gather the facts before you plan. Nehemiah went out by night and looked at the broken walls of Jerusalem himself before he told the leaders what he meant to do (Nehemiah 2:12-17).
Ask why, more than once
Toyota made a habit of asking “why?” about five times, to get from a symptom to a cause. The dishwasher will not drain. Why? The filter is clogged. Why? Plates go in with food on them. Why? Nobody scrapes them. Fix that and the clog stops coming back. It has limits: one chain of whys tends to stop at one cause when a problem has several, and two people can reach different answers (five whys and its critics).
Four steps
George Pólya, a maths teacher, set out four steps in his 1945 book How to Solve It: understand the problem, make a plan, carry out the plan, look back. Halving is a plan. Looking back is the step most people skip: did it work, and what would make it faster next time?
Watch: a step-by-step troubleshooting method
This lesson comes from a course for computer repair exams, and it sets out the same habit as a checklist. Its last step is the one Pólya called looking back: write down what you learned.
Where you’ll meet this
| The problem | Define it | Simple things first, or split it |
|---|---|---|
| The lamp will not turn on | Is it this lamp only, or the whole room? | Plug, switch, a bulb you know works. Then try a working lamp in the same outlet. |
| A string of lights is dark | The whole string, or one section? | Test half the string, then half of that half. |
| A leaking faucet | Does it drip from the spout, or leak at the handle? | Close the shut-off valve under the sink before you open it up. A drip from the spout points to the washer or cartridge; a leak at the handle, to an O-ring or packing. |
| The dishwasher will not drain | Water left after a full cycle? Since when? | Clean the filter in the bottom, look for a kink in the drain hose, and run the garbage disposal if it drains into one. |
| Wi-Fi is slow | Everywhere, or one room? One device, or all of them? | Restart the router. Then test right next to it: if it is fast there, the problem is the Wi-Fi reach, not the line into the house. |
| A recipe that failed | Flat, dense, burnt, too salty? At which step? | Next time change one thing only, so you learn what fixed it. An oven thermometer tells you if the dial is right. |
| A maths word problem | What is asked? What is given? | Draw it. Try a smaller case. Then look back: does the answer make sense? |
What Scripture says
If the ax is blunt, and one doesn’t sharpen the edge, then he must use more strength; but skill brings success.
Ecclesiastes 10:10In context. The Teacher: a blunt ax takes more strength, but skill brings success. Sharpening first is the wise move.
I went out by night by the valley gate, even toward the jackal’s well, then to the dung gate, and inspected the walls of Jerusalem, which were broken down, and its gates were consumed with fire.
Nehemiah 2:13In context. Before telling anyone his plan, Nehemiah rides out at night to inspect Jerusalem’s broken walls and burned gates.
Then went I up in the night by the brook, and inspected the wall; and I turned back, and entered by the valley gate, and so returned.
Nehemiah 2:15In context. He keeps inspecting the wall in the dark, then returns. Only afterward does he tell the leaders what he means to do (2:17).
It is the glory of God to conceal a thing, but the glory of kings is to search out a matter.
Proverbs 25:2In context. It is God’s glory to conceal a matter and the glory of kings to search it out.
The heart of the discerning gets knowledge. The ear of the wise seeks knowledge.
Proverbs 18:15In context. The discerning heart gets knowledge, and the wise ear goes looking for it.
Watch
Use it on your choice
A choice starts the same way as a repair: say it in one plain sentence before you weigh anything. Walk me through it begins there.