A student can do forty UKMT questions and still freeze when a problem asks for structure. We built three daily puzzles to train that habit in five minutes — not another worksheet stack.
A student can sit forty UKMT questions and still freeze when a problem asks for structure — digit constraints, a grid that must balance, an expression built under fixed rules.
More past papers does not fix that gap. Neither does another times-tables app.
We see it every season: bright children who recognise topics but cannot hold constraints in mind long enough to finish an unfamiliar argument. That is not a syllabus problem. It is a thinking-habit problem.
In early February 2026 we shipped three daily maths puzzles on problems.cc: Cryptarithm, Magic Square, and Summit. This is what we wanted them to do — and how we think they fit into serious competition preparation.
Why daily, not random
Olympiad preparation already has enough randomness: which paper you open, which question type appears, whether you panic on question 15.
Daily puzzles are deliberately not that.
Each game releases one shared puzzle per UK calendar day. Everyone gets the same challenge. Siblings can compare approaches. A parent can set a five-minute ritual before homework without printing another worksheet.
Miss a day? The archive keeps every past puzzle playable. No account is required to start; sign in later if you want streaks and calendar history synced.
We borrowed the rhythm from the best daily puzzles — short, repeatable, slightly addictive — but aimed the content at logic, not arithmetic speed.
What we were optimising for
Most maths products sit at two extremes:
| Extreme | What it trains | Where it fails |
|---|---|---|
| Drill apps | Fluency, speed | Almost no constraint reasoning |
| Full olympiad papers | Deep proof work | Too heavy for a daily habit |
We wanted something in the middle: five minutes of deliberate structure that still feels like a game.
For competition students, that means:
- Constraint reasoning — unique digits, fixed sums, allowed operations only
- Pattern sense — symmetry in a grid, opposite cells, centre invariants
- Operational fluency — building an expression under order-of-operations rules, not just calculating an answer
Not syllabus coverage. Not “more questions”. A different kind of repetition.
The mistake we see in preparation
Take a typical JMC-aiming student who only does timed papers. They get fast at recognising types. Under pressure, they still abandon systematic search halfway through — or they guess because checking uniqueness feels tedious.
Another student spends five minutes on a cryptarithm before homework. Same ability band. Different behaviour on an unfamiliar digit puzzle in a paper: they list what each letter cannot be, they test one column at a time, they notice when two constraints collide.
That shift is small. It compounds.
Daily puzzles are not a substitute for past papers or teaching. They are a low-friction way to practise the habits papers assume you already have.
The three games
| Game | Link | Core habit |
|---|---|---|
| Cryptarithm | problems.cc/games/cryptarithm | Digit constraints and uniqueness |
| Magic Square | problems.cc/games/magic-square | Balancing structure in a 3×3 grid |
| Summit | problems.cc/games/summit | Building expressions to hit a target |
Cryptarithm — crack the code
A classic letter-for-digit puzzle: each letter stands for a unique digit, leading letters cannot be zero, and the vertical addition must work.
This is detective work, not school arithmetic. Students learn to propagate constraints — if two letters share a column, what does that force elsewhere? — and to verify that a partial assignment still has a unique completion.
We draw from a curated pool of dictionary words, checked for valid solutions. Each UK date selects deterministically from that pool so the puzzle is stable for the whole day.
Cryptarithm is the only daily game with a pausable solve timer. Share your time when you finish, or ignore the clock entirely.
Want more after the daily? The cryptarithm library goes deeper.
Magic Square — balance the grid
Fill a 3×3 grid with nine consecutive numbers so every row, column, and diagonal sums to the same total. A few cells are given as hints.
The magic sum changes by date, so memorising one template does not carry you far. Students learn centre placement, opposite pairs, and when symmetry collapses the search space.
Estimated solve time is modest — often under fifteen minutes — which makes it a gentle daily habit rather than a weekend project.
Summit — find the operations
Countdown-style: you are given digits in fixed order and must insert +, −, ×, ÷ (and sometimes brackets) to reach the target.
Weekday variety keeps it from going stale: some days allow full operations; others restrict to + and ×; others introduce brackets. We track move count on solve — no timer, but you still feel whether your approach was efficient.
Summit trains the same mental muscle as “make 24 from these numbers”, but with validated puzzles and shapes that rotate through the week.
How a day works
- Open the games hub — three tiles, one puzzle each.
- Play today’s puzzle for your UK calendar date (we use Europe/London so “today” matches British families and schools).
- Finish, or save a draft and return later; progress can live in the browser until you sign in.
- Browse the monthly archive calendar to replay past days — solved, started, and untouched days are colour-coded.
Confetti on solve is intentional. Short wins matter when the rest of olympiad prep is long and uneven.
How we build each day’s puzzle
We did not hand-pick three hundred puzzles and hope for the best. Each game has a generation rule tied to the date:
- Cryptarithm — deterministic selection from a verified pool (same date → same puzzle everywhere).
- Magic Square — procedural construction: start from a classic template, vary the magic sum, rotate and reflect, then choose 2–4 hint cells so the puzzle stays fair but not trivial.
- Summit — shape chosen by weekday, then digits and target sampled until a puzzle with a small number of valid solutions emerges; we reject broken or ambiguous boards.
The point is consistency without boredom: shared daily ritual, but enough variety across the month that students cannot coast on one trick.
How to use them in a prep week
- Pick one game as a warm-up — five minutes before homework or past-paper work. Rotate through the three across the week.
- Finish before you peek — treat a daily like a micro-competition: full attempt, then review what constraint you missed.
- Name the habit — “I rushed the uniqueness check” beats “I got it wrong”.
- Keep past papers for depth — dailies train structure; papers train stamina and proof length.
- Use the archive on quiet days — no guilt for missing Tuesday; replay it Thursday.
That is a different model from “do every past paper in order”. Closer to how we would train a musician: isolate the habit, repeat it briefly, then perform the longer piece.
Why we built this on problems.cc
Exact Science treats preparation as a maths education lab. problems.cc is where practice lives — past papers, curated sets, and now a daily layer that does not replace them.
We think competition maths needs more than worksheets and less than dumping full olympiad problems on a twelve-year-old. Daily puzzles sit in that gap: logic training parents can structure, students can enjoy, and coaches can point to without another PDF.
Try today’s three puzzles at problems.cc/games. Five minutes each. Same puzzles as everyone else in the country. See what changes when structure becomes a habit, not an accident.