Maths that makes you think.

Real problem-solving in maths for Years 3–13, week by week — with step-by-step solutions and a tutor that builds thinking, not memorising. Physics coming soon.

Try this week's set → See how a week works

Year 4 · Number · Reasoning

A snail is at the bottom of a well that is 10 metres deep. Each day the snail climbs up 3 metres. Each night, while it sleeps, it slides back down 1 metre. The snail starts climbing on Monday morning. On which day does it first reach the top and crawl out?

The trapIt looks like 10 ÷ (3 − 1) = 5. The number is right — but for the wrong reason. Change the well to 12 m and that shortcut breaks.

Track itEach full day-and-night cycle nets +2 m. End of day 4 the snail is at 9 m, then slides to 8 m overnight.

The idea that mattersThe last day is special. On day 5 the snail starts at 8 m and climbs 3 → 11 m — past the top. It's out, so it never slides back. Always check the final climb on its own.

AnswerIt escapes on day 5 — a Friday.

The tutor

It gives hints. It never gives the answer.

Anyone can hand a child the answer — a worksheet key, a leaderboard, an AI. That teaches nothing. PhysMat's tutor does the opposite: it asks the next good question, and stops one step short of solving it for them.

ChildIs it just 10 ÷ 2 = 5 days?

PhysMat tutorBefore we trust that — picture the very last day, when the snail reaches the top during daytime. Does it still slide back down that night?

ChildNo… once it's out, it's out.

PhysMat tutorExactly. So try writing down its height at the end of each day, and watch for the first day it climbs past 10. What do you get?

A real hint ladder — strategy, then a sub-step, then a near-solution — that by design never states the final answer. The child gets unstuck, not carried.

Whether you're at home or in the classroom

One bank of beautiful problems. Two ways to use it.

For parents

Enrichment your child will actually enjoy — not another worksheet grind.

A fresh set of real problems every week, Years 3 to 13.
Step-by-step solutions you can follow, even if maths isn't your thing.
A tutor that builds thinking instead of handing over answers.

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For schools & teachers

A ready-to-set enrichment programme that adds nothing to your workload.

Curriculum-aligned across KS2, KS3, GCSE and A-level.
Every problem ships with a worked method and the common mistakes — the prep is done.
Ideal for maths clubs, stretch tasks and able pupils.

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One ladder, age 7 to 18

The same idea grows with your child.

Year 6

KS2 · a counting puzzle

There are 8 children at a birthday party. Every child shakes hands exactly once with every other child. How many handshakes happen in total — and why isn't it 8 × 8 or 8 × 7?

No one shakes their own hand, and every handshake is counted twice. So 8 × 7 ÷ 2 = 28.

same idea

Year 12

A-level · a quadratic

At a conference, every delegate shakes hands once with every other. In total 276 handshakes take place. How many delegates attended?

n(n − 1) / 2 = 276 → n² − n − 552 = 0 → n = 24.

The handshake a 10-year-old counts is the quadratic a 16-year-old solves. One canon of problems, from Year 3 to Year 13.

Tap a year to try a real problem from that level.

Physics — coming soon

Year 6 · KS2 · The pigeonhole idea

A drawer holds 6 red, 8 blue and 10 green socks, all mixed up, in a completely dark room. How many socks must you take to be certain of 3 of the same colour — no matter how unlucky you are?

Imagine the unluckiest draw: 2 of each colour is 6 socks with no triple. One more must complete a colour. So 7 socks.

How a week works

A calm weekly habit — not a race.

Get the set

A new set of carefully chosen problems lands each week, matched to your child's year.

Wrestle with it

They think it through. When they're stuck, the tutor nudges — a question, not an answer.

Unfold the thinking

Then the worked solution, step by step: the method named, and the mistakes to avoid.

Classic problems, not drill

Problems worth thinking about — some of them centuries old.

These aren't auto-generated worksheets. They're the classic problems mathematicians have loved for generations — chosen because the thinking they ask for is beautiful.

Tap a family to read one.

Year 7 · A problem Tolstoy set

A team of mowers had to mow two meadows, the larger twice the size of the smaller. For half a day the whole team worked the larger meadow. Then it split in half: one half finished the larger meadow by evening, the other started the smaller and didn't quite finish. The next day a single mower finished the remaining piece in a full day. How many mowers were on the team?

Measure in mower-days, and a paragraph of prose collapses to one line — 8 mowers. Leo Tolstoy wrote it for fun; a twelve-year-old can crack it.

The proof of a maths product isn't a logo wall. It's whether the maths is any good.

So we put it on the page. Thousands of problems across nine age groups, Years 3 to 13 — each with a full worked solution, the method named, and the common mistakes spelled out. Try one before you decide.