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.
Opposite And Adjacent Faces Across Two Views
A dice puzzle shows two views of the same die and asks which number lies opposite a given face. Standard dice opposite pairs always sum to seven — one faces six, two faces five, three faces four — and no two adjacent views can share a face.
How To Solve Dice Puzzles
- List what each view shows.
- Use the seven rule: opposite faces sum to seven on a standard die.
- A face seen in both views is adjacent to everything the other face touches.
- Eliminate positions where a shown face would have to be its own opposite.
- Deduce the remaining face by elimination.
The seven rule settles most of the die before any rotation: if you can see three faces, you already know all six..
| Family | What it covers |
|---|---|
| The seven rule | On a standard die opposite faces sum to seven, which answers a whole class of questions with arithmetic instead of imagination. |
| The hidden face | Three faces are visible and three are not. Work out what is underneath. |
| Two views | The same die photographed twice. Everything seen beside a number touches it, so the number never seen beside it is opposite it. |
| Three views | More views, more constraints — and the chance to pin down the whole die. |
| Impossible views | Which of these pictures could not be the same die as the first? |
| Standard or not | Not every die in a puzzle obeys the seven rule. Spot the ones that do not. |
Two Views Are Enough
Two views of a standard die pin down every face, because each view adds adjacency facts and the seven rule supplies the opposites. The explanations here walk that deduction face by face, so you can check your own reasoning against 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.