The format
What one puzzle looks like
Every puzzle in both books is built from only the digits 1, 2 and 3. No other number appears anywhere — not in the questions, not in the answers. That single constraint is what makes the books work, and it is why a calculator is no help at all.
12 − 3 = 11
The equation is false. Swap any two digits — one move, nothing added, nothing erased — and make it true.
13 − 2 = 11
Trade the 2 and the 3. It is the only swap on the card that works — and that word only is the whole point of the book.
◻³ = 1331
Each blank holds a number built from 1, 2 and 3. No calculator, and no trial and error needed.
11³ = 1331
A cube ending in 1 must have a root ending in 1, and 1331 is far too small for 21. The answer is settled before any cubing happens.
The point
What it trains: deduction
Most arithmetic practice rewards one thing — getting the number out fast. That skill has been fully automated. What has not been automated is looking at a statement and working out what must be true about it. That is deduction, and it is what these two books drill, one card at a time.
12 − 3 = 11
Watch the reasoning, not the arithmetic.
“The right side is 11, so it cannot move — it has no other digit to trade with that keeps it small. So the fix is on the left. Twelve minus three is nine; I need eleven, so the left side has to grow by two. Swapping the 1 and the 2 gives 21 − 3, far too big. Swapping the 2 and the 3 gives 13 − 2 — eleven. Done, and nothing else could have worked.”
13 − 2 = 11
Three or four sentences of pure elimination, and one subtraction at the very end. That ratio is the design.
- Elimination comes before arithmetic. With only three digits and one legal move, a child can hold every possibility in their head at once. The search is small enough to reason about instead of grinding through — which is exactly when reasoning starts to feel easier than guessing.
- Uniqueness forces a reason. Each Junior card has exactly one swap that works. A child who lands it by luck still has to explain why the others fail, and that explanation is the actual lesson. “It works” becomes “it must work, and nothing else can.”
- Structure beats speed. The Senior puzzles are settled by shape — last digits, size, whether a number can possibly be a square or a cube — long before anything is computed. This is the first taste of the idea that you can know an answer without calculating it.
- It transfers. Ruling out three wrong options on a test, finding the one line that broke the program, working out who could not have done it in a story — same move. Deduction is one skill wearing different clothes, and this is a low-stakes place to practise it.
The way in
Start with the free sampler
Six puzzles — three from each book — with the full answer key and the method shown. It costs nothing, it prints on plain paper, and it takes about ten minutes at a kitchen table. If a child leans in, the books will land. If they do not, you have lost nothing.
Teachers: the same sampler is posted as a free resource on my Teachers Pay Teachers store, alongside both full books with terms of use and answer keys included.
The books
Two editions, two ways in
Junior hands you a false equation and one move to repair it — a gentle warm-up in seeing structure. Senior withholds pieces and lets structure tell you what belongs there, ramping from “2 + 1 = ◻” up to a hard set built on squares and cubes. Fifty puzzles each, every solution verified, answer keys included.
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.
- Just 123, properly introduced — what is in it, and how it builds deductive thinking. (you are here)
- 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.
Take the sampler, try it on a child, and tell me where they got stuck. That is the most useful thing anyone sends me.