Dice Basics — Opposite Faces

🎯 Learning Objective

Find opposite faces of a dice from one or two views, and tell a standard dice from an ordinary one.

💡 Concept

• A dice has 6 faces; two faces seen together in one view are ADJACENT, never opposite
• Standard dice: the numbers on two opposite faces always add up to 7 (1-6, 2-5, 3-4)
• Ordinary dice: opposite faces need NOT add to 7 — decide only from the views given
• Two-common-faces rule: if two views share TWO common numbers, the two odd (non-common) numbers are opposite
• One-common-face rule: keep the common face fixed and rotate mentally to place the rest
• A single number can never sit on two faces of the same dice

🧮 Key Formulas

Standard dice: opposite faces sum to 7 (1+6, 2+5, 3+4)

✏️ Easy Example

Q. On a standard dice, the number 2 is on top. What number is on the bottom?

1. Standard dice: opposite faces sum to 7
2. Bottom = 7 − 2

Answer: 5

🇮🇳 Real-Life Example

Every Ludo dice at home is a standard dice — that is why the number facing up and the one hidden at the bottom always add up to 7.

📝 Exam-Level Example

Q. Two positions of the same dice show the faces (1, 2, 3) and (1, 3, 5). Which number is opposite to 2?

1. Common numbers in both views: 1 and 3
2. The non-common numbers are 2 and 5
3. By the two-common-faces rule, 2 and 5 are opposite

Answer: 2 is opposite to 5

📝 Exam-Level Example

Q. In one throw, a dice shows 3, 4 and 5 on its three visible faces. Can 3 be opposite to 5?

1. 3, 4, 5 are all visible together → they are mutually adjacent
2. Adjacent faces are never opposite

Answer: No — 3 and 5 are adjacent, so they cannot be opposite

🪄 Memory Trick

Two common faces across two views? The two leftover numbers are opposite. And anything you can see together in one view is adjacent, so never opposite.

⚠️ Common Mistakes

• ❌ Assuming every dice is standard — apply the sum-7 rule only when 'standard' is stated
• ❌ Calling two faces opposite when they appear together in a single view
• ❌ Forgetting to look for the two common faces across the two given positions

🏆 Exam Tips

• ✅ First scan both views for the common faces — they unlock the opposite pair
• ✅ On a standard dice, if you know one face you instantly know its opposite (7 − face)

📌 Summary

• Faces seen together are adjacent, never opposite
• Standard dice: opposite faces sum to 7
• Two common faces → the two odd faces are opposite
• Ordinary dice: judge only from the given views