The Infinite Hotel
Can a full hotel with infinitely many rooms still fit more guests? Wrestle with infinity and discover how mathematicians compare endless sets.
Macmillan Academy · More-Able Programme
Stretching challenges, competitions worth entering and brilliant things to read — chosen to push curious minds across Years 7 to 13.
🧠 Dilemma of the week
A machine could give you a lifetime of perfect, happy experiences — but none of it would be real. Would you plug in? And what does your answer reveal about what you truly value?
See it in full & browse the archive →📖 Word of the week
Lasting for only a very short time; fleeting.
“The ephemeral beauty of the cherry blossom lasts barely a week.”
From the Greek ephēmeros, 'lasting only a day'. Your challenge: use it correctly this week.
Curriculum & beyond
Stretching tasks that go beyond the lesson — built to deepen thinking, not just move faster. Each is mapped to the national curriculum, and the selection refreshes each half-term.
Can a full hotel with infinitely many rooms still fit more guests? Wrestle with infinity and discover how mathematicians compare endless sets.
Retell a fairy tale from the antagonist's point of view. Explore narrative perspective, sympathy and the unreliable narrator.
Plan a fair test you could actually run on Mars. Account for gravity, atmosphere and temperature — then defend your method.
Should museums return contested artefacts? Build a balanced argument using real case studies and primary sources.
A university-admissions-style problem. Less about the answer, more about constructing a watertight proof.
Spend a whole essay analysing a single complex sentence. A degree-level skill — how much meaning can one line hold?
Break a series of codes that get harder each time, then design one of your own that a friend can't crack.
Design consistent grammar rules for a made-up language — a real taste of how linguistics works.
Choose six works around a single theme and write the gallery notes. Think like a critic and a curator.
2026/27 diary
Real competitions worth entering across the year — tap any title for the official page. Month-only entries are confirmed by the organiser nearer the time.
National 90-minute problem-solving challenge for Years 11–13. High scorers progress to the Senior Kangaroo and the British Mathematical Olympiad.
A free national codebreaking competition from the University of Southampton, now in its 25th year. Crack a new cipher each week as 'The Mystery of the Missing Silver' unfolds. Enter alone or as a team — registration is open now, the first challenge lands on 8 October, and the prize-giving is at Bletchley Park.
Free competition for 14–19s: answer 'Which milestones have most significantly defined the UK's constitutional journey?' with a poster or a video of up to three minutes. Entries close 9 October.
The National Gallery's public-speaking prize for ages 16–19: a ten-minute illustrated talk on any work of art, artefact or building you choose. Free — the school registers in the autumn; heats and finals run January to March.
Christ Church, Oxford's poetry prize for 16–18 year-olds — free to enter, one poem of up to 48 lines on a set theme, with a first prize of £5,000. The 2027 competition opens in October; the theme and deadline will be announced by Christ Church.
Free computational-thinking challenge run in school over two weeks each November. Open to all year groups — logic puzzles, no coding needed. Runs 9–20 November 2026.
A family of national physics challenges: Round 1 for Year 13 each November, the Senior Physics Challenge for Year 12 in March, and the Junior Physics Challenge for Year 10 in late spring. Dates confirmed by the organiser.
Team cyber-security challenge for girls in Year 8 — codebreaking, logic and digital forensics. Now part of the NCSC's TechFirst programme; registration opens in the autumn.
Two short online papers for Year 12–13 biologists, with questions well beyond A-level. Run in school each January; your school registers entrants.
The Royal Society of Chemistry's flagship challenge for Years 12–13: a written Round 1 paper sat in school in late January, with top performers invited on towards the International Olympiad. School registration opens mid-September.
Queen's College, Oxford's national translation competition for ages 11–18, in six languages. Translate a real poem or story creatively — no perfect fluency needed. The 2027 competition opens on 25 January, with free practice packs released through the autumn.
Problem-solving challenge for Years 9–11, with follow-on Kangaroo and Olympiad rounds for the top scorers.
Solve language puzzles using pure logic — no prior knowledge of the languages needed. Free, with four levels from KS2 to KS5; sat in school in early February.
A public-speaking competition for Years 10–13: a five-minute speech answering this year's question — "How does your local environment help us to understand national and global histories?" Heats run from autumn to the national final in spring.
EngineeringUK's free STEM project competition for ages 11–18 — enter a science, engineering or technology project individually or as a team. The 2026 round closed in early March; 2027 dates confirmed by the organiser.
The national poetry recitation competition for schools in England — learn a poem by heart and perform it, with categories for ages 11+, 14+ and 16+ and a grand finale at Shakespeare's Globe. Free; entries close in early April.
Write anything — essay, story, poem, reportage — responding to an annual theme, for ages 12–18. The new theme is announced each October, with an optional draft-feedback round before the final spring deadline.
The Royal Society of Biology's online challenge for Years 9–10 — a short multiple-choice paper sat in school each spring, rewarding curiosity about the natural world beyond the curriculum. Dates confirmed by the organiser.
Problem-solving challenge for Years 7–8 — the entry point to UKMT's family of competitions.
A 90-minute written paper for Year 12 chemists, set well beyond A-level and run in school each June after AS exams.
The Royal Economic Society's writing prize for Years 10–13 — a short blog post or five-minute media entry answering a set economic question. No economics study needed; entries due early summer, with the final in October. Confirm the deadline on the organiser's site.
The UK's leading poetry competition for ages 11–17. Free to enter, up to three poems each — deadline midnight 31 July 2027; entries open in the autumn. (Entries must be your own work, not AI-generated.)
Read to study, not to skim
Challenging texts chosen to reward effort. Each pick comes with a note on what to look for — plus a challenge rating, and whether the stretch lies mainly in its language or its ideas.
📚 Every book suggested below is available to borrow from the school library — go and grab one!
Engineering, resilience and ingenuity. Ask: what makes someone solve a problem no one else could?
The whole of science, made gripping. Notice how big ideas were actually discovered.
Comic and effortless on the surface — underneath, a feast of satire, philosophy and very big ideas, in a completely different genre to the rest. Read for the jokes; stay for the questions.
Why are some countries rich and others poor? Test the argument against examples you know.
A sweeping story of humankind. Where is the author interpreting rather than reporting?
Far less known than Lord of the Flies — and far tougher. An unfamiliar viewpoint and deliberately fractured language reward perseverance, asking what really makes us human.
How we really make decisions. Spot your own biases as you read.
A landmark in biology. Separate the science from the metaphor.
Moral philosophy through real dilemmas. Where do your instincts break down?
More ways to stretch
Deeper challenges for curious minds — dig into any of these.
A dilemma of the week, fallacies to spot, and reasoning challenges.
Explore →Pick a question, follow the scaffold, and produce something of your own.
Explore →Big questions that bridge subjects — maths in music, the ethics of AI.
Explore →Practice problems for the big competitions.
Coming soonBrilliant work from students rising to the challenges — take a look.
Explore →KS5 · aim high
Stretch toward university — admissions-test practice, plus where your subjects can take you next.
Sitting STEP, TMUA, ESAT, MAT or PAT? Apex is our interactive coach — adaptive practice that targets your weak topics, progressive hints leading to full worked solutions, timed mock exams, and topic-by-topic progress tracking. Links to genuine past papers throughout.
Open the Apex coach ↗Free taster programmes, lectures, work experience and guidance to help you aim high — and find where your subjects can lead.