A standard double-nine domino set contains 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 that figure.
Understanding Domino Sets
Dominoes are rectangular tiles with two square ends, each end displaying a number of pips (dots). A double-nine set includes all possible combinations of pips from zero to nine on each end. This means you'll find dominoes like 0-0, 0-1, 0-2, all the way up to 9-9.
Calculating the Number of Dominoes
We can use combinations from mathematics to calculate the total number of dominoes. Specifically, we're looking at the number of combinations of selecting two numbers from a set of ten numbers (0 through 9), where the order doesn't matter (a 3-5 domino is the same as a 5-3 domino).
The formula for combinations is: n! / (r! * (n-r)!)
Where:
- n is the total number of items in the set (10 in this case, representing the numbers 0-9)
- r is the number of items we are choosing at a time (2 in this case, because each domino has two ends)
- ! represents the factorial (e.g., 5! = 5 * 4 * 3 * 2 * 1)
Applying the formula:
10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45
This gives us 45 dominoes. However, this doesn't account for the double dominoes (like 0-0, 1-1, 2-2, etc.). We need to add those ten dominoes (one for each number from 0 to 9) to get the final answer.
45 + 10 = 55
Therefore, a standard double-nine domino set has a total of 55 dominoes.
Why is it 55 and not another number?
The total number of dominoes in a set depends on the highest number present. For a double-N set, the total number of dominoes is given by the formula: (N+1)(N+2)/2. When N=9, the formula yields: (9+1)(9+2)/2 = 10*11/2 = 55. Thus confirming the 55 dominoes in a double nine set.
What about other types of domino sets?
You can also find domino sets with different highest numbers. For example:
- Double-six: These sets contain (6+1)(6+2)/2 = 28 dominoes.
- Double-twelve: These sets contain (12+1)(12+2)/2 = 91 dominoes.
This knowledge provides a clear understanding of how the number of dominoes scales with the highest number on the tiles.
I hope this comprehensive explanation answers your question completely!
