A double-nine domino set contains a total of 55 dominoes. This might seem like a lot, but understanding the math behind it reveals why. Let's break down how we arrive at that number.
Understanding Domino Tile Combinations
A domino tile is defined by two numbers, typically represented by dots or pips. In a double-nine set, each number can range from 0 to 9. The key is that each possible combination of two numbers is represented only once. This means you won't find two dominoes with the same numbers, regardless of their order.
For example, you'll have a [0-0], a [0-1], a [0-2], and so on, all the way to a [0-9]. But you only have one [1-2] - it's the same as a [2-1] – only one of those is in the set.
The Calculation
To figure out the total number, we use a mathematical combination formula. For a double-nine set (where the highest number is 9):
- Consider the number of choices for the first number: There are 10 options (0 through 9).
- Consider the number of choices for the second number: This depends on the first number. If the first number is 0, there are 10 options for the second. If the first number is 1, there are 9 options (we don't want duplicates like [1-1], which we already counted as [1-1]), and so on.
This leads to a calculation like this: 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 55
Alternatively, we can use the formula for combinations: (n + 1)(n + 2) / 2, where 'n' is the highest number. With n = 9, this becomes (9 + 1)(9 + 2) / 2 = 10 * 11 / 2 = 55
Why It's Not Just 10 x 10 = 100
It's a common misconception to think there are 100 dominoes (10 numbers x 10 numbers). However, this doesn't account for the fact that [1-2] is the same as [2-1], eliminating duplicates.
What about other domino sets?
The same principle applies to other domino sets. A double-six set (the most common smaller set) has (6+1)(6+2)/2 = 28 dominoes. A double-twelve set would have (12+1)(12+2)/2 = 91 dominoes, and so on.
How many dominoes are in a double-9 set? The answer is 55. This number is reached using combinations and not simple multiplication.
Hopefully, this clear explanation answers your question completely! Let me know if you have any more domino-related questions.
