7th Grade · Ages 12–13
The Slowest-Two Year
Twelve is when a child can be shown that the sensible plan — always take the cheapest next step — is a trap with a name.
- 1 Hard Thing
- 5 days · 105 minutes
- 3 unmarkable questions
The Hard Thing · about a grade above
The Bridge at Night
Four people must cross a rickety bridge in the dark. Only two can be on it at once, and whoever crosses must carry the one torch. They walk at 1, 2, 5 and 10 minutes. A pair moves at the slower person's pace, and somebody has to walk the torch back each time. Get all four across in 17 minutes.
Stuck for ten minutes? Good. Open one hint, not three.
1Hint 1
The obvious plan is to let the fastest walker ferry everybody. Work out exactly what that costs.
2Hint 2
The ten-minute walk cannot be avoided. The real question is whether the five-minute walk has to be paid for separately.
3Hint 3
What if the two slowest crossed together?
The answer — only after you have written something down
1 and 2 cross (2 minutes). 1 walks back (1). 5 and 10 cross together (10). 2 walks back (2). 1 and 2 cross (2). Seventeen. The fastest-ferries plan costs 19, because it pays for the 10 and the 5 as two separate crossings. Sending the slow pair together buys the 5 for free.
The genius move
“Pair the expensive things together so you only pay for one of them.”
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
The Bridge at Night. Find the 19-minute plan first; it is meant to be found.
25 min - TuesdayBuild
Write the 19 and the 17 side by side and mark the exact crossing where they diverge.
25 min - WednesdayRead up
Read how a delivery company decides what order to visit addresses in, and why it is hard.
20 min - ThursdayTeach
Teach the 19 first. Let them believe it. Then show the 17.
15 min - FridayBreak
Invent a fifth walker whose speed changes the shape of the answer. Prove it does.
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
When is the obvious plan the wrong plan?
- ?2
Is there always a best answer, or only a best-so-far?
- ?3
How do you know when to stop looking?
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
Four walkers, 17 minutes.
Next year
Any number of walkers, and the rule for deciding which pairing to use.
The year after
Greedy algorithms and why they fail — the same idea that runs inside a satnav.
What lives on the desk this year
- Index cards, one per person in the puzzle
- A whiteboard you can wipe without guilt
- A timer
- A folder of plans that did not work, kept on purpose
- A list of problems you intend to come back to
The rest of 7th Grade
One hard thing a day is the sharp end. It sits on top of an ordinary year.
Last updated: September 2026