Concept 5 of 9
Cubes & Dice: Opposite Faces
Today's big idea
Opposite faces of a standard die always add to 7, so one face names its partner.
Two visible faces still leave left and right able to swap.
How it works
👀 What's going on?
A die sits on the table showing one number, and the question asks about a face you cannot see. One fact settles most of those questions.
💡 Here's the trick
Look at the dice above. Opposite faces of a standard die always add to 7, so 1 sits across from 6, 2 from 5, and 3 from 4.
🪄 How to do it
- 1.Read the visible number on the dice above.
- 2.Subtract it from 7 to get the face directly opposite.
- 3.Repeat for any second face you are given.
✍️ Try it
A die shows 2 on top; what is underneath? Then: a die shows 6 at the front; what is at the back?
7 minus 2 gives 5 underneath. 7 minus 6 gives 1 at the back.
⚠️ Watch out
You might be thinking two visible faces pin down all the rest. They do not. Knowing the top and the front still leaves left and right able to swap, unless the question says which way round the die is built.
🌟 Why this matters
Every board game uses these dice, and the total-of-7 rule is what lets you name a face without picking the die up.
Exam tip: All six faces add to 21, which cracks questions about the four sides at once.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“On a standard dice, the TOP face shows 4. What is on the BOTTOM?”
- 1
Recall the dice rule
Opposite faces sum to 7. 🎲
- 2
Compute the bottom
7 − 4 = 3
- 3
Answer ✓
3
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
On a standard dice, opposite faces sum to 7 (1↔6 · 2↔5 · 3↔4). Bottom = 7 − top.
DICE · ROUND 1 OF 3
Quick check
✅ VERIFICATION
The six faces of a die add to 21. If the top is 6 and the bottom is 1, what do the four side faces add to?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Figure Rotation
Track one corner through the turn. 90° CW: up → right.