Dice Puzzles
What is on the face you cannot see? Which number is opposite the four? Could these two pictures be the same die at all? Sixty patterns across six question types, with the deduction worked out after every attempt — including why each wrong option fails.
Also known as dice problems and cubes and dice — the same puzzle under two names.
Working Out The Face You Cannot See
A dice puzzle shows one or more views of a die and asks what lies on a hidden face, which faces are opposite, or whether the die shown could exist at all. The usual shortcut is that opposite faces add to seven — but plenty of dice break that rule, which is why elimination from the visible faces is the method that always works.
The Two Rules That Solve Almost Everything
Dice questions look like they need three-dimensional imagination. Most of them do not — they need two facts and a bit of elimination.
- Opposite faces sum to seven. On a standard die: 1–6, 2–5, 3–4. If a question says the die is standard, this answers it with arithmetic and no visualisation at all.
- The faces always total 21. Every die carries 1 to 6 exactly once, whatever the pairings, so the hidden faces always total 21 minus the visible ones. This one holds even when the die is not standard.
Do not assume the seven rule. Puzzle setters use non-standard dice deliberately, and several patterns here do too. If you are given two views, the die is usually telling you it does not want you to take seven for granted — otherwise one view would have been enough.
| Rule | What it says | When it holds |
|---|---|---|
| Opposite faces sum to seven | 1 opposite 6, 2 opposite 5, 3 opposite 4 | On a standard die only |
| Elimination | Anything seen beside a face is NOT opposite it | Always — it needs no assumption |
| Two views of one die | Four faces adjacent to a repeated face rule out the rest | Always |
| Non-standard dice | The seven rule fails outright | Which is why elimination is the method worth learning |
| Handedness | Three faces meeting at a corner have a fixed chirality | Always — it is what makes a picture impossible |
Two Views: The Elimination Method
This is the real skill, and it works on any die, standard or not:
- Find the number in both pictures. That is your anchor face.
- List everything shown beside it. Anything appearing in the same picture as the anchor must share an edge with it.
- Count to four. A face on a die touches exactly four of the other five. Once you have seen four different numbers beside the anchor, you are done looking.
- Take the leftover. The one number you never saw beside the anchor is the only face that does not touch it — and the only face that never touches a given face is the one opposite it.
When A Picture Of A Die Is Impossible
Three separate things can make a drawn die impossible, and they are worth checking in this order because the first two cost no imagination:
- A repeated number. Every face of a die is different, so the same number twice is an instant fail.
- Two opposite faces visible. A die shows at most three faces and they all meet at one corner. Opposite faces point in opposite directions, so they can never both show.
- The wrong handedness. The subtle one. Three faces that do meet at a corner can still be drawn the wrong way round — swap the two front faces and you have the mirror image of the die, which no real die can be turned into.
The Six Question Types
- The seven rule — one view of a standard die, and arithmetic does the rest.
- The hidden face — what is underneath, or which three numbers are out of sight.
- Two views — the elimination method, and the heart of this item type.
- Three views — more constraints, enough to pin down the whole die.
- Impossible views — which picture could not be the same die.
- Standard or not — deduce a pair, then judge whether the seven rule holds.
When The Seven Rule Stops Working
On an ordinary die, opposite faces add to seven — so a 1 is opposite a 6, and anything you can see beside a face is definitely not opposite it. That shortcut solves a great many dice puzzles and then fails badly, because plenty of dice are not standard. Several puzzles here break the seven rule deliberately, which forces the method that always works: everything you can see next to a face touches it, so whatever is left over is opposite it. Elimination beats the shortcut every time it disagrees with it.
Dice Puzzles Frequently Asked Questions
Do opposite faces always add up to seven?
On a standard die, yes: 1–6, 2–5, 3–4. But puzzle dice are not always standard, and several patterns here deliberately break the rule. Two views are usually a hint that you are meant to deduce the pairing rather than assume it.
How do two views help?
Everything shown beside a number touches it, and a face touches exactly four others. So the number never seen beside your anchor face is the one opposite it.
What is handedness and why does it matter?
Three faces meeting at a corner can be drawn in two arrangements, and only one of them is a real die — the other is its mirror image. It is the hardest flaw to spot, and the one this site's hardest patterns are built on.
How many puzzles are there?
There is no fixed number. Each puzzle is rebuilt from the short seed in the page address, so the supply is effectively unlimited.
What is the rule about opposite faces on a die?
On a standard die the numbers on opposite faces add up to seven: 1 with 6, 2 with 5, and 3 with 4. That single fact answers a whole family of questions with arithmetic instead of visualisation. Not every die in a puzzle is standard, though, so check before you rely on it.
How do I work out the opposite face from two views?
Find the number that appears in both views. Everything shown beside it in either picture must touch it. A face on a die touches exactly four of the other five, so once you have seen four different numbers beside it, the one number you have never seen beside it is the one opposite it.
Why can a die never show two opposite faces at once?
A die shows at most three faces from any viewpoint, and those three all meet at one corner. Opposite faces point in exactly opposite directions, so they can never both be visible. Any picture showing both is impossible.
How many dots are there on a die altogether?
Twenty-one. The faces run 1 to 6, and 1+2+3+4+5+6 is 21. It also falls out of the seven rule: three pairs of opposite faces, each pair adding to seven, gives 3 × 7 = 21. That is a quick way to check a die you have been shown from several angles actually adds up.