Analogical Problem Solving

after Gick & Holyoak (1980, 1983)

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Before you start

A reading task, then a problem to solve.

This takes about fifteen minutes. There are two parts, and they are scored separately.

Work through it in one sitting, and please don't look anything up or ask anyone — including a chatbot. The result only tells you something if you go in cold. There are no trick questions and nothing here is timed against you, though the page does quietly record how long each part takes.

Everything you type stays in your browser. Nothing is sent anywhere. At the end you'll get a summary you can copy and bring to your session.

Your name or student ID Optional — this just labels the summary at the end.

Begin

Part one · Reading

Read the passage.

Read carefully. When you're done you'll be asked to retell it from memory — the passage will disappear at that point — so read for the shape of what happens, not the details.

Passage A · The General

A small country was ruled from a strong fortress at its center. The fortress sat in the middle of the country, surrounded by farms and villages, and many roads radiated out from it like spokes on a wheel.

A general resolved to capture the fortress. He knew that an attack by his entire army would take it easily — his force was more than strong enough. But he learned that the dictator had mined every road.

The mines were set so that small groups of men could pass over them safely, since the dictator needed to move his own troops and workers. Any large force, however, would detonate them. That would not only destroy the road, it would devastate the neighboring villages.

The general could not send his whole army down any one road. So he divided the army into small groups and sent each group to the head of a different road. When everything was ready, he gave the signal, and each group marched down its own road. Every group reached the fortress at the same moment. In this way the general captured the fortress.

Passage B · The Fire Chief

An oil well in the desert caught fire and burned out of control. The blaze was enormous, and the nearest fire station was a long way off.

The fire chief arrived to find that the only water nearby was a lake a short distance away. He had one large hose, and the townspeople who had come to help had brought dozens of small buckets.

The chief tried the obvious thing first. He ran the large hose from the lake and aimed a heavy stream at the base of the fire. The stream was powerful, but it could only cover part of the blaze at once, and the flames kept moving around it. Nothing was gained.

Then the chief had an idea. He told every villager to fill a bucket and form a ring completely around the well. On his signal, all of them threw their water at the same instant, from every side at once. The fire went out immediately.

Retell it in my own words The passage disappears when you press this.

Passage hidden. Write it from memory — that's the part being measured.

What happened in the passage? A few sentences is plenty. If you've forgotten a detail, skip it and keep going.

What do these two passages have in common? Not the setting — the two stories have nothing to do with each other on the surface. What is the same about how each problem gets solved?

Continue

Short break

Clear your head for a moment.

A quick unrelated task. Rate each word for how pleasant it feels to you. There are no right answers and this isn't scored.

Continue

Part two · Problem

Here is the problem.

Suppose you are a doctor treating a patient with a malignant tumor in his stomach. Operating is impossible, but unless the tumor is destroyed the patient will die.

There is a kind of ray that can destroy the tumor. If the rays reach the tumor all at once at a high enough intensity, the tumor is destroyed. Unfortunately, at that intensity the healthy tissue the rays pass through on the way in is destroyed as well.

At lower intensities the rays are harmless to healthy tissue — but they leave the tumor untouched.

What procedure could be used to destroy the tumor with the rays without destroying the healthy tissue around it?

Describe your solution. Take as long as you want. If you're stuck, write down what you've tried and why it doesn't work — that's real data too. How confident are you that your solution would actually work?

50%

Submit solution

One question first

While you were working on that, did anything come to mind?

Be honest either way — there's no better answer here, and this question is the whole point of the activity.

NoI worked on the problem by itself. Something did, but I couldn't say whatA feeling that I'd seen something like it, without being able to place it. Yes — something specific from earlier in this activityI can name what it was.

What came to mind, and did you use it?

Continue

Second attempt

Try the problem once more.

Hint

In solving this problem, you may find that the passage you read earlier suggests a solution.

The tumor is in the stomach. Operating is impossible. High-intensity rays destroy the tumor but also the healthy tissue they pass through. Low-intensity rays are harmless to tissue but don't affect the tumor.

How can the tumor be destroyed without harming the healthy tissue?

Your solution now. If it hasn't changed, say so — that's a legitimate answer.

Submit and see the answer

The answer

Send many weak rays from many directions at once.

Each ray is too weak to harm the tissue it passes through. They all converge on the tumor, and only there do they sum to full strength.

One full-strength ray

Many weak rays, converged

Why the passage was relevant

In the passage	In the problem

Nothing on the left resembles anything on the right. Armies aren't rays and fortresses aren't tumors. What carries across is the structure: a force that must arrive whole at one point, but cannot travel whole along any one path. That's what an analogy actually transfers — not the things, the relationships between them.

Score my answers

Scoring

Mark your own answers honestly.

Nobody sees this but you and whoever you show it to. An inaccurate score here just makes the result useless.

Your first attempt — before the hint

Your second attempt — after the hint

See my result

Result

Your result

What this experiment found

Gick and Holyoak ran this in 1980. Given the passage and then the problem with no hint, roughly a third of people produced the converging-rays solution. Told that the passage might help, roughly three-quarters did.

The knowledge was already there in both groups. What the hint supplied wasn't information — it was retrieval. The gap between those two numbers is the size of a problem that has nothing to do with how smart anyone is.

Which is why the 1983 follow-up matters

Gick and Holyoak went looking for something that would raise unhinted transfer. What worked was giving people two stories from unrelated domains and asking them to say what the two had in common. Comparing two cases forces the shared structure into the open, where a single case leaves it buried under its own details. One example teaches the example. Two examples teach the pattern.

Take this with you

Copy this summary and bring it to your session.

Copy summary Start over

Notes for whoever is administering this

Conditions. Add a query string to the link to set which version a student gets:

• ?c=one — single source passage (the General). This is the default and the canonical 1980 condition.
• ?c=two — both passages plus the comparison prompt. The 1983 schema-induction condition. Expect higher unhinted transfer.
• ?c=control — no passage at all. Baseline solution rate for the problem by itself, with the hint step skipped.
• ?c=random — assigns one of the three at random and records which.

The measure. The number that matters is not whether they solved it. It's unhinted versus hinted. A student who converges only after the hint has the knowledge and lacks the retrieval cue — which is precisely what a calendar, a notes system, or a worked-example file is for. That reframe is the point of running this.

Verbatim answers are in the summary. Self-scoring is unreliable in both directions, so the export includes everything they typed. Score it yourself against the convergence criterion: multiple lower-intensity rays, from different directions, arriving at the tumor simultaneously. Partial credit is worth tracking — "operate through the esophagus" and "lower the intensity and go slowly" are the classic non-convergence answers and both show real problem-solving.

No data leaves the browser. This page has no backend. If you want responses collected automatically, the export block is plain text and can be posted to a form endpoint with about ten lines of JavaScript — but as written, nothing is stored or transmitted, which is also why a student can close the tab and lose everything. Tell them to copy the summary before they leave.

Don't reuse it on the same student. Like any transfer problem, it works exactly once.

Adapted from Gick, M. L., & Holyoak, K. J. (1980), Analogical problem solving, and (1983), Schema induction and analogical transfer. The tumor problem is originally Duncker's (1945). Passages here are retellings, not the original texts.