Before you solve anything, you decode. These first four steps are pure decoding, no answers yet. Detectives do not arrest the first suspect they see.
Read it twice
Once for the story (what is going on here?), once for the maths (what numbers and words matter?). Slow is smooth, smooth is fast.
Hunt the question
Find the one thing it is actually asking and underline it. Usually it hides near the end, after a "how many", "find", or "what is". Everything else is just clues.
Grab the clues
Circle every number, and write its unit next to it (dollars, weeks, cm). A number with no unit is a clue with no fingerprints.
Translate to goblin-maths
Turn the words into symbols using the Goblin Translation table below. This is where the traps live, so go slowly.
Tiny steps
Now you can solve. One small step at a time, each on its own line. If a step feels big, it is really two steps wearing a coat.
Sniff test
Read your answer back into the story. Right size? Right unit? Could it really happen? If it smells off, it probably is.
These are the moves we say out loud in a session. The routine above is the first three skills in action. The rest keep you on track while you solve, and bank what you learned for next time.
1 · Open the Case
Read twice, hunt the question, grab the clues. Set the case up before you touch a number.
"Detectives don't arrest the first suspect."
2 · Check the Case Files
Have I seen a case shaped like this? Is it a Tank, a Crossover, a Container, or a Backwards case?
"Your journal is your case-file archive. Flip back through it."
3 · Pick Your Gadget
Choose a tool and say why: a table, a diagram, an equation, or working backwards.
"Which gadget fits this case, and what makes you sure?"
4 · The Three Knocks
The big one. Mid-case, stop and check you are still on the right path. Details below.
"What am I doing? Why? Is it helping?"
5 · Sniff Test
Estimate first, check the units, read the answer back into the story. Does it make sense?
"Would that actually happen in real life?"
6 · Case Notes
What kind of case was it? What did I try first? What got me unstuck? Write it for Future Kelcy.
"What would you want to know next time you meet this case?"
This is the skill that matters most, so it gets its own desk. When you feel stuck, or you have been scribbling for a while with no progress, you knock three times.
Knock, knock, knock.
Three questions, every time you get that stuck feeling:
If the answer to number three is "no", that is not a disaster. Backing out of a dead end and trying a new gadget is a detective skill, not a mistake.
English words point to maths symbols. Most are friendly. A few are traps, marked in red. The big one: "less than" flips the order, so read it carefully.
| When the case says... | Goblin-maths | Watch out |
|---|---|---|
| sum, total, altogether, more than, increased by | + | "5 more than x" is x + 5. Adding is friendly, the order does not matter. |
| difference, less than, take away, reduced by, fewer | − | TRAP 🌶️ "5 less than x" is x − 5, NOT 5 − x. "Less than" flips the order. |
| product, times, of, double, triple | × | "double a number" is 2x. "of" with a fraction or percent also means times. |
| quotient, per, shared between, split, each | ÷ | Check which number goes on top. "shared between 4" means ÷ 4. |
| is, equals, gives, results in, the same as | = | "the same as" can mean a Crossover: set two expressions equal to each other. |
| per week, each hour, every day | rate (gradient) | A steady rate is a Tank Case. This is your m in y = mx + c. |
| to start, already has, at the beginning | start value (y-intercept) | The head start everyone forgets. This is your c in y = mx + c. |
| how many, find, what is, work out | the question | This is what you are solving for. Underline it in step 2. |
🌶️ The reversal trap, up close
"7 less than double a number is 23" becomes 2x − 7 = 23. It is tempting to write 7 − 2x, because 7 comes first in the sentence. But "less than" tells you to subtract it from the other thing. Whenever you see "less than" or "fewer than", slow right down and check the order.
Remember: dead ends are clues. If you pick the wrong gadget and it does not work, you have not failed, you have just crossed one suspect off the list. Knock three times, pick a new gadget, keep going. That is exactly what real detectives do.