How Many Dominoes Are in a Double-Nine Set?
A 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 explore why.
Understanding Domino Sets
Dominoes are characterized by their double-sided tiles, each side displaying a number of pips (dots). A "double-nine" set means the highest value on any tile is nine pips. The set includes all possible combinations of numbers from zero to nine.
The Calculation
To figure out the total number of dominoes, we use a combination calculation:
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Consider the pairs: We need to find the number of unique pairs of numbers from 0 to 9 that can be placed on the domino tiles. This includes pairs like (0,0), (0,1), (1,1), (0,2), and so on.
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Apply the combination formula: The formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items (in this case, 10 numbers from 0 to 9) and r is the number of items we choose at a time (2, since each domino has two sides).
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Calculation: Using the formula, we get 10C2 = 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45. This represents the number of dominoes with different numbers.
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Adding the Doubles: We haven't yet accounted for the double dominoes (0-0, 1-1, 2-2...9-9). There are 10 of these.
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Total Dominoes: Adding the 45 unique pairs and the 10 double dominoes gives us a grand total of 45 + 10 = 55 dominoes.
Why are there 55 dominoes in a double-nine set? This addresses some common questions.
This calculation accurately determines the number of dominoes needed to have all possible combinations of numbers from 0 to 9. It's a concise and precise method that avoids needing to list out and count every single domino.
What about other domino sets?
The same principle can be used to calculate the number of dominoes in other sets:
- Double-six: This set (numbers 0-6) has 28 dominoes.
- Double-twelve: This set (numbers 0-12) has 91 dominoes.
The formula allows you to calculate the number of dominoes in any double-n set efficiently.
Hopefully, this comprehensive explanation clarifies the answer and provides a deeper understanding of the mathematics behind domino set sizes.
