1 + 23 = 23
False as written. Don't calculate — rearrange. Nothing may be added and nothing erased.
1 + 2³ = 3²
1 + 8 = 9. Same three digits, same order on the left — two of them simply climbed. This one opens the free Just 1·2·3 lesson.
If you felt the small click of that landing, you already know why I do this. The click is not a reward for being quick at arithmetic. It is deduction — the answer arriving before the calculation does.
I spent a career as a research scientist, and I have spent the last fifteen years filling notebooks with math for the pleasure of it, most of it drafted on foot on the same few miles of road every morning. That habit led me to a conclusion I now build everything around: children do not dislike math. They dislike the version of math that only rewards speed.
The philosophy
Four things I hold to
- Deduction before calculation. The valuable skill in an age of machines is not computing an answer — a phone does that. It is looking at a statement and knowing what must be true.
- Math lives outside the page. Mine comes off mailboxes, house numbers, street signs, garage doors and clock faces on the morning walk. A problem set in something real is a problem worth solving.
- Always show a worked example. No book of mine sends you in cold. Method demonstrated, then the ladder, then the challenge. Being stuck should be a choice.
- Constraints are the fun. Give a child every digit and every operation and you get homework. Give them three digits and one move, and you get a game.
Puzzle books
Start here: Just 123
The first book in the line takes that last idea to its limit. Every puzzle is built from only the digits 1, 2 and 3. No other number appears anywhere. Three digits sound like nothing — they are enough for fifty puzzles a volume, and enough to keep an adult standing still on a sidewalk.
Two editions, two ways in. Junior gives you a false equation and one move to repair it. Senior withholds pieces and lets structure tell you what belongs there.
12 − 3 = 11
The equation is false. Swap any two digits — one move — and make it true.
13 − 2 = 11
Trade the 2 and the 3, and 13 − 2 = 11. It is the only swap on the card that works — every other trade leaves it false, which is what makes it a deduction rather than a guess.
◻³ = 1331
Each blank holds a number built from 1, 2 and 3. No calculator, and no trial and error needed.
11³ = 1331
The answer is legible before you cube anything: a cube ending in 1 must have a root ending in 1, and 1331 is far too small for 21. Senior ramps from “2 + 1 = ◻” to the hard set with squares and cubes.
111 × 111 = ?
Nothing to repair here. Just look at what comes out.
111² = 12321
A staircase up and back down, built from nothing but ones — and it stays inside our three digits. Its smaller sibling is 11² = 121, and 1 + 2 + 3 = 1 × 2 × 3 = 6, the only run of counting numbers that adds and multiplies to the same place.
In the store
Take one home
The series
What is coming
Seven posts, one idea each — the books, the method behind them, and the road they were written on.
- Make Math Fun Again — and Just 123, where three digits are enough. (you are here)
- Just 123, properly introduced — what is in it, and how it builds deductive thinking.
- Deduce Me! — twenty-five square-number riddles, and why a riddle teaches faster than a drill.
- Math on the walk — mailboxes, speed-limit signs and garage doors as problem surfaces.
- One move, or two — the move family explained, and how to compose your own.
- Puzzles that need no reading — colour and shape as a way into arithmetic before literacy.
- Life in my Math County — the whole map, and where each book sits on it.
If any of this is your kind of thing, take a free lesson, try it on a child, and tell me where they got stuck. That is the most useful thing anyone sends me.