1st Grade · Ages 6–7
The Smaller-First Year
Six is old enough to be handed a problem that is too big for them — as long as they are handed the tool for shrinking it at the same time.
- 1 Hard Thing
- 5 days · 105 minutes
- 3 unmarkable questions
The Hard Thing · about a grade above
The Handshake Problem
Five people are in a room. Every person shakes hands with every other person exactly once. How many handshakes happen altogether?
Stuck for ten minutes? Good. Open one hint, not three.
1Hint 1
Do not start with five. Start with two people — how many handshakes?
2Hint 2
Now three. Now four. Write your answers in a row and look at them.
3Hint 3
Your answers jump by 1, then 2, then 3. Work out what each new person is adding.
The answer — only after you have written something down
Ten. Two people make 1 handshake, three make 3, four make 6, five make 10 — because every new person shakes hands with everyone already in the room, so you add 1, then 2, then 3, then 4.
The genius move
“When a problem is too big, do the tiny version first.”
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 Handshake Problem, starting at two people.
25 min - TuesdayBuild
Draw the five people as dots, join every pair with a line, count the lines. Same answer, different language.
25 min - WednesdayRead up
Read something with a number in the title that you cannot quite handle yet.
20 min - ThursdayTeach
Teach the dots-and-lines picture to somebody who has not heard the problem.
15 min - FridayBreak
Guess the answer for six people before working it out. Then work it out. Was your guess high or low, and by how much?
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
Can you be alone in a room and still shake hands?
- ?2
If everybody in your school shook hands, would it take an hour or a day?
- ?3
Why does adding one more person add so many handshakes?
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
Five people, worked up from two.
Next year
Ten people — 45 — and the moment you stop drawing lines and start adding.
The year after
The formula n(n−1)/2, which you will meet again at fifteen and recognise on sight.
What lives on the desk this year
- Plain paper, no lines on it
- Coins to stand in for people
- A ruler for the joining lines
- A jar for the questions nobody could answer
- A pencil with a rubber you are allowed to wear out
The rest of 1st Grade
One hard thing a day is the sharp end. It sits on top of an ordinary year.
Last updated: September 2026