Skip to the challenge
WHITE ROOMBY DUEMELLO

ROOM 00 / AN OPEN PROBLEM

Almost is
not enough.

Three numbers. Four diagonals. A problem with
no known solution. Dare to find the first?

Enter the unsolved room ↘

NO VERIFIED SOLUTION KNOWN

THE PERFECT CUBOIDUNSOLVED ≠ PROVEN IMPOSSIBLE

A ROOM THAT REFUSES TO FIT

Make every line whole.

3 / 4 WHOLE DIAGONALS
A box with three edge lengths and four diagonals to test. Illustration is not to scale.ABCNOT TO SCALE / ALL ANGLES 90°
Choose three positive whole-number edge lengths

An Euler brick: three faces work. Now for the fourth line.

Testing here is free exploration. Only an explicit cash entry can increase the prize.

START FROM AN ALMOST

Your recent experiments 0

THE BOUNTY / ONE ROOM. ONE PRIZE.

Four out of four.
Or the room stays closed.

Find positive whole-number edges that make every diagonal a whole number. A valid new solution earns the prize under the published rules. Free entry, with no scheduled closing date.

Checking cash entry status…

£1,000 starting prize. +£1 per qualifying unsuccessful account, up to £5,000. The live status below confirms when submissions are available.

See the prize rules ↓

CLEAR RULES / VERSION 2026–03

No hidden doors.

Unsolved is the challenge.
A genuine solution is welcome.

01 What has never been solved?

No verified perfect cuboid is currently known: a rectangular box with positive integer edges, three integer face diagonals and an integer space diagonal. Its existence remains an open mathematical problem. That does not prove it is impossible. There is no guarantee anyone will find a solution or win. Status checked 20 October 2026. Read the research ↗

02 £1,000 → £5,000. How does it grow?

One cash prize starts at £1,000. The first server-verified unsuccessful cash entry from each challenger account adds £1, until the prize reaches £5,000. Further entries from that account add nothing. One person may use only one account. Accounts are the counting unit, not a claim that we have identified every unique person.

Warm-ups, local tests, shared moves, refreshes, abandoned attempts and invalid inputs never add money. At 4,000 qualifying unsuccessful accounts the prize stays at £5,000. A network retry uses the same entry reference and never counts twice. Up to 12 unsuccessful cash entries per account per hour are accepted; new-account requests are limited to five per network address per hour.

03 What would win?

The first eligible cash entry recorded in the server ledger with three positive integers for which A²+B², A²+C², B²+C² and A²+B²+C² are all perfect squares qualifies for verification. Exact integers are checked; rounded decimals do not qualify. The server serialises submissions, so its recorded order resolves simultaneous entries. A valid discovery must not be rejected to keep the room unbeaten. A proof of non-existence is not an entry for this construction challenge.

The web checker accepts up to 1,000 digits per edge. For larger candidates, email info@wedigitliz.com with your account ID and the three integers as a text file. Never send your access key. WeDigitlize will arrange exact checking and register a passing candidate against your account, issuing a receipt. Manual candidates take priority from that ledger registration, not the email timestamp; an email alone is not an accepted entry. Keep your calculation and receipt. This route is free.

04 Who can enter? When does it end?

UK residents aged 18 or over may enter, excluding the promoter’s staff, immediate families and anyone involved in running the challenge. Entry is free: no purchase, subscription or donation, and buying anything gives no advantage. Mathematical software and collaboration are allowed. A team agrees its representative before entry; the single prize goes to the eligible submitting account, not every room participant.

One person, one account. No email address or phone number is required to create an account or submit on the website. Your private access key is the only way to recover it. Keep that key safe. Winner eligibility and account control are checked separately.

There is no scheduled closing date. Entries open when the live status says “open” and continue until a verified eligible solution wins. Entries pause while a candidate is reviewed or the service is unavailable. A pause does not erase receipts, reset the prize or remove a valid claim. No end date is used to delay review or payment.

05 Who reviews and pays?

WeDigitlize Ltd handles reviews and payments. The first passing candidate reserves the displayed prize and pauses new entries. A receipt is issued immediately; it is a claim for review, not confirmation that money has been paid. Contact info@wedigitliz.com with your receipt reference to arrange eligibility checks and payment. Do not email your private access key or bank details in your first message.

WeDigitlize aims to review a complete claim within 14 days, explains any delay and gives a written decision. The promoter checks the exact arithmetic, account control, age, UK residence and the published eligibility rules. An accepted eligible claim is paid in GBP by an agreed payment method within 30 days of acceptance. There is no claim fee. A rejected claim receives reasons; the prize reopens at the same amount. No automated cash transfer occurs on submission.

You can ask WeDigitlize to reconsider a rejection within 14 days of receiving the decision, using the same support address and receipt reference. Mathematical decisions must follow the four exact checks, and a qualifying construction cannot be rejected merely to avoid paying the prize. Your statutory rights are unaffected.

06 Promoter, records and contact

Promoter: WeDigitlize Ltd, registered in England and Wales, company 17465598. Registered office: Crown House, North Circular Road, London, England, NW10 7PN. Contact: info@wedigitliz.com.

Entry receipts, review decisions and completed-payment records are kept so claims can be checked. Read our privacy notice for retention and your rights. The status and receipts in your signed-in account are the source for your entry’s result. Local animations and the guide’s commentary never award a prize.

NEED A ROOM WITH A KNOWN WAY OUT?

Four free warm-ups.

Blackout. One Last Line. The Quiet Lock. The Missing Piece.

Choose a warm-up ↗

THE GUIDE / A VERY SIMPLE QUESTION

Can you build this box?

  1. Choose three positive whole numbers for the edges A, B and C.
  2. Test the three face diagonals and the line through the box. All four must also be whole numbers.
  3. Try a near miss, change an edge, and compare the exact checks. The rules never change.

44 × 117 × 240 gives three whole face diagonals: 125, 244 and 267. The space diagonal is not whole. No verified set passing all four is known.

YOUR CHALLENGER ACCOUNT

One key.
No inbox.

No email or phone number. Your private access key restores your account and cash entry receipts.

One person, one account. New accounts become available when cash entries open. Signing in again ends other sessions for this account.