Concept 7 of 8
Dice: Opposite Faces Add to 7
Today's big idea
Opposite faces of a dice add to 7, so a hidden face is 7 take away the one you see.
Only the face directly across matters, so the other numbers are decoration.
How it works
👀 What's going on?
A dice is sitting on the table showing a 4, and you are asked what is underneath it without picking it up. There is a rule built into every ordinary dice that answers it instantly.
💡 Here's the trick
Look at the dice above. Faces on opposite sides always add up to 7, so 1 sits across from 6, 2 from 5 and 3 from 4. Knowing one face therefore tells you the one hidden behind it. The hidden number is simply 7 take away the one you can see.
🪄 How to do it
- 1.Read the number on the face you are given, as marked on the dice above.
- 2.Take it away from 7.
- 3.That answer is the face directly opposite it.
✍️ Try it
A dice shows 3 on top, so what is underneath? Then: a dice shows 5 on top and 2 facing you, so what is on the face at the back?
Seven take away three is 4 underneath. For the second, the back is opposite the face you can see, so it is 7 take away 2, which is 5. The 5 on top has nothing to do with it.
⚠️ Watch out
You might be thinking the numbers you can see must be added somehow. They do not interact. Each face pairs only with the one directly across from it, so a question about the back is answered by the front alone.
🌟 Why this matters
Board games run on this without anybody mentioning it. It is the same reasoning as working out what is hidden behind any solid object.
Exam tip: Ask which face the question is really opposite to, since the other numbers are usually there to distract.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“A dice shows 3 on top. What number is on the bottom face?”
- 1
Recall the rule
On a dice, opposite faces always add to 7. 🎲
- 2
Subtract from 7
7 − 3 = 4
- 3
Answer ✓
bottom = 4
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
On a standard dice, opposite faces add to 7 (1↔6 · 2↔5 · 3↔4). Bottom = 7 − top.
DICE · ROUND 1 OF 3
Your turn: 7 − 2 = ? (the bottom face)
Quick check
✅ VERIFICATION
A dice shows 2 facing you and 6 on top. What is on the face at the back?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Spot the Odd Figure
Pick a feature, sweep the row, stop when one disagrees.