Lesson 1 of 3 · Dice: views, opposite faces and open nets
Opposite face rule
Cubes and Dice · for IPMAT Indore, IPMAT Rohtak and JIPMAT · asked in JIPMAT 2026
The exam method
- If two remain, use the clockwise reading from a common face (PW and afterboards solutions use the same rule).
Worked examples
Rohtak 2020: dice drawn with sides showing (3, 6), (6, 3) and (1, 5); opposite faces add to 7; each of these has an even number on top. Total on top?
Solution: 8. The top is neither a visible face nor its opposite: (3, 6) leaves 2 or 5 → 2; (6, 3) → 2; (1, 5) leaves 3 or 4 → 4. 2 + 2 + 4 = 8.
JIPMAT 2025: four views show (2, 3, 6), (5, 2, 4), (6, 3, 1), (3, 5, 1). What is opposite 3?
Solution: 4. 3 is seen with 2, 6, 1 and 5, so the face it never meets, 4, is opposite.
Watch out
- Over-using 'cannot be determined': with a common face and the clockwise rule, two views usually fix all three pairs.
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