How Many Dominoes Are in a Double-Nine Set?
A standard double-nine domino set contains a total of 55 dominoes. This might seem like a random number, but there's a simple mathematical explanation behind it.
Let's break down how we arrive at this number:
Understanding Domino Sets
A domino is defined by two numbers, typically represented by pips or dots. In a double-nine set, the highest number on any domino is nine. The dominoes range from double-blank (0-0) to double-nine (9-9).
Calculating the Number of Dominoes
The calculation isn't as straightforward as simply multiplying 9 by 9. This is because a domino with a 2 and a 5 is the same as a domino with a 5 and a 2. To avoid counting duplicates, we use a combinatorial approach.
We can think of this as selecting two numbers from a set of 10 possible numbers (0 through 9) with replacement (we can choose the same number twice, as in a double-domino). The formula for combinations with replacement is:
(n + k - 1)! / (k! * (n - 1)!)
Where:
- 'n' is the number of options (10 in our case, from 0 to 9).
- 'k' is the number of selections (2, since each domino has two numbers).
Applying this formula:
(10 + 2 - 1)! / (2! * (10 - 1)!) = 11! / (2! * 9!) = (11 * 10) / (2 * 1) = 55
Therefore, there are 55 dominoes in a standard double-nine set.
What About Other Domino Sets?
The same principle applies to other domino sets. For example:
- Double-six: (6 + 2 -1)! / (2! * (6 - 1)!) = 21 dominoes
- Double-twelve: (12 + 2 - 1)! / (2! * (12 - 1)!) = 91 dominoes
Why are Dominoes Important?
Beyond their simple elegance, dominoes are a versatile tool. They're used for:
- Games: From simple matching games to complex strategic ones.
- Mathematics education: Illustrating concepts like probability and combinations.
- Creative expression: Creating intricate chain reactions and mesmerizing displays.
This comprehensive guide should answer any questions you have about the number of dominoes in a double-nine set. It's a deceptively simple question with a surprisingly elegant mathematical answer.
