Did you ever observe the numbering patterns in a rolling dice and wonder why is it that way? Did you ever wonder why on earth probability problems in any book reads like, "rolling a fair or balanced dice"?
Any standard 6 sided dice is designed such that the sum of numbers on the opposite sides will be seven -- 6+1, 5+2 and 4+3.
This design is a combination of 2 important factors - fairness and balance.
- Fairness: Each number on the die (1-6) should have an equal chance of landing face-up when rolled. The way the opposite sides add up to 7 ensures this. Imagine the die as six equal-sized triangles joined at their corners. Any two opposite triangles will always have numbers that add up to 7. This means no matter how the die lands, a specific number landing face-up doesn't affect the likelihood of another number coming up next time.
- Balance: The die should land randomly and not be biased towards favoring any particular side. The opposite sides summing to 7 helps with this too. The weight distribution of the pips (dots) is roughly the same on all sides, and the opposing numbers balance each other out, contributing to a more stable roll.
So, the simple rule of opposite sides adding up to 7 on a die isn't just a fun fact, it's a clever design element that ensures random and fair outcomes, making it the perfect tool for games and activities that rely on chance.
This pattern exists not just for six-sided dice, but for many other types of dice with different numbers of sides. Now as an exercise try thinking what would be the sum of opposite sides for a 10 sided fair and balanced dice?