4th Grade · Ages 9–10
The Three-Answer Year
Nine is old enough to be told that a question has a size — and that you can work out whether a plan can possibly work before you try it.
- 1 Hard Thing
- 5 days · 105 minutes
- 3 unmarkable questions
The Hard Thing · about a grade above
Eight Coins, One Light
Eight coins look identical. One is fake and slightly lighter. You have a balance scale — the kind with two pans — and you may use it twice. Find the fake.
Stuck for ten minutes? Good. Open one hint, not three.
1Hint 1
Do not start with 4 against 4. First ask what a weighing can actually tell you.
2Hint 2
A balance has three results, not two: left down, right down, or level. Level is information too.
3Hint 3
Try leaving some coins off the scale altogether.
The answer — only after you have written something down
Weigh 3 against 3. If one side rises, the fake is in that three — weigh one of them against another, and if those balance it is the third. If the first weighing comes out level, the fake is one of the two you left off, so weigh those two against each other.
The genius move
“Count the answers before you count the coins. Two weighings times three results is nine possible outcomes, and you only need to tell eight coins apart.”
Five days, five muscles
The week
Never the same muscle two days running. The weekend is not on this list on purpose — being bored is the sixth muscle and it needs two clear days.
- MondayThe Hard Thing
Eight Coins. Insist on two weighings, not three.
25 min - TuesdayBuild
Build the balance: a coat hanger, two cups, string. Test it with real coins and a folded paper fake.
25 min - WednesdayRead up
A newspaper written for adults. Find one number in it and decide whether you believe it.
20 min - ThursdayTeach
Teach the three-results idea. It is one sentence long and it is the whole puzzle.
15 min - FridayBreak
Can you do 9 coins in two weighings? Can you do 10? Find the exact place it breaks.
20 min
Start Monday now
Read the problem once more, out loud, and press start. Solving it is not the measurement.
Nothing rung today yet
The twenty-five minutes
Four phases. The middle one is most of it, and it is meant to feel slow.
- 1SitRead the problem again, out loud. Write nothing yet.
- 2AttackTry the wrong thing. It is faster than thinking about the right one.
- 3StuckWrite down the exact place you are stuck. “I don’t get it” is not a place.
- 4LogOne sentence: what you will try tomorrow. Then close the book.
No answer key
Three questions you cannot mark
Ask one at dinner. Do not resolve it. A question that survives the washing-up is doing its job.
- ?1
How much can you learn from one question?
- ?2
Is guessing ever the best strategy?
- ?3
With 27 coins, how many weighings would you need?
Where this goes
The ladder
The same idea, three times, roughly a year apart. This is what depth looks like from the outside.
This year
Eight coins, fake known to be lighter.
Next year
Twelve coins where you do not know whether the fake is heavy or light. The same counting argument says three weighings, and it is right.
The year after
The idea underneath: information has a size, and you can measure it before you have the answer.
What lives on the desk this year
- A balance you built yourself
- Identical coins and one that is not
- Paper wide enough for an outcome tree
- A stopwatch
- A wall for the things you got wrong
The rest of 4th Grade
One hard thing a day is the sharp end. It sits on top of an ordinary year.
Last updated: September 2026