Hamster Opera
A mathematical game of musical hamsters — and a two-thousand-year-old problem with no known general solution.
Support & Classroom GuideA mathematical game of musical hamsters — and a two-thousand-year-old problem with no known general solution.
Support & Classroom GuideAbout the Game
Hamster Opera is a game built around one of mathematics' most enduring puzzles. A line of singing hamsters takes turns performing — but any hamster who sings off-key is eliminated. The question is always the same: which hamster survives?
The game is designed to help young people discover the beauty and elegance of mathematics — not by memorizing formulas, but by playing, observing patterns, and reasoning toward abstraction.
The Josephus Problem — named after the first-century historian Flavius Josephus — asks: given n people standing in a circle, eliminating every k-th person, which position survives? Mathematicians have studied this problem for over two millennia. Though an elegant closed form solution exists for k=2 (every 2nd person eliminated) a general closed form solution has not been found after two millennia of study — a beautiful example of how deep mathematics can hide inside a simple game.
For Families & Educators · Ages 9–18
Whether at the kitchen table or in a classroom, these activities mirror how mathematicians actually work — moving from physical experience to pattern recognition to abstraction. Parents and children can work through them together, and each step builds naturally on the last.
Have everyone stand in a line — family members, friends, or classmates. Each person says their number aloud and steps forward if they would survive the current round. Run multiple rounds with different values of n. The last person standing wins. Making the problem physical lets children feel the elimination pattern before they analyze it.
Assign students n = 1 through 15 as homework. For each value, they write out a line of numbers and cross off positions one by one until one remains. Record the winning position. This slow, deliberate work builds intuition that no amount of explanation can replace.
Review the completed table together. Ask: What do you notice? Are there any values of n where the winning position is always 1? Let children propose conjectures before confirming anything. Parents don't need to know the answer — the goal is shared observation, not answer-giving. Genuine curiosity is more valuable than expertise.
| n (hamsters) | Winning position |
|---|---|
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 | |
| 11 | |
| 12 | |
| 13 | |
| 14 | |
| 15 |
Based on the table, ask your child to propose an algorithm that generates the winning position for any n. Hint if needed: What is special about the winning numbers? The pattern connects directly to binary representation — a beautiful bridge between a human puzzle and the language of computers, and a moment of genuine discovery that families can share.
For advanced students: what happens when every k-th hamster is eliminated, not just every 2nd? Develop an algorithm for the general case of n hamsters and k interval. For k=2 a closed-form solution exists, but for arbitrary k no closed-form solution has been found — even after two millennia of study. Students working on this are genuinely touching the frontier of mathematics.
Support
What age is Hamster Opera designed for?
The game is suitable from around age 9 through high school and beyond. The core gameplay is accessible to younger children, while the underlying mathematics rewards older players and curious adults. It is designed to be played together — a parent and child will get more out of it than either would alone.
Does the game collect any personal data?
No. Hamster Opera does not collect, store, or transmit any personal data. All game state is stored locally on your device.
Is Hamster Opera free?
Pricing information is available on the App Store listing.
I found a bug. How do I report it?
Please email us at inquiries@ntuple.com with a description of the issue, your device model, and iOS version. We read every report.
Can I use Hamster Opera in my classroom?
Absolutely — it works beautifully in both settings. Hamster Opera is well suited for classroom use across grades 4 through 12, and works equally well at home where parents and children can explore the mathematics together at their own pace.
Get in Touch
Questions, bug reports, feedback from families and teachers, or just a note about a hamster that won against the odds — we read everything.
inquiries@ntuple.comPrivacy Policy
Effective date: April 2026
Hamster Opera is developed by Internautica, Inc. This privacy policy explains what data the app does and does not collect.
Data we do not collect. Hamster Opera does not collect, store, transmit, or share any personal information. The app does not require an account, does not track your location, does not access your contacts or photos, and does not contain advertising or third-party analytics.
Data stored on your device. Game progress and settings are stored locally on your device only. This data never leaves your device and is not accessible to Internautica, Inc. or any third party.
Children's privacy. Hamster Opera is designed for use by children and adults alike. Because we collect no data whatsoever, there are no special privacy risks for younger users.
Changes to this policy. If this policy changes in the future, we will update the effective date above and post the revised policy here.
Contact. Questions about this privacy policy can be directed to inquiries@ntuple.com.
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