How Many Dominoes in a Double-Nine Set?
A double-nine domino set contains 55 dominoes. This number isn't arbitrary; it's derived from a simple mathematical formula. Let's explore why.
Understanding the Dominoes
A domino is essentially a rectangular tile divided into two squares, each displaying a number of pips (dots). In a double-nine set, the numbers range from zero to nine. Each square can show any number within this range.
Calculating the Total
To understand how we arrive at 55, consider the following:
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Pairs of numbers: We have numbers from 0 to 9, which is 10 different numbers. For each number, we can pair it with itself (e.g., 6-6) and with every other number (e.g., 6-0, 6-1, 6-2... 6-9).
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Combinations: This means that for each number, we have 10 potential pairings. However, we're double-counting (the 3-4 domino is the same as the 4-3 domino). To account for this, we must use combinations rather than permutations.
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The Formula: The mathematical formula for combinations is nCr = n! / (r! * (n-r)!), where n is the total number of items and r is the number of items we're choosing at a time. In our case, n = 10 (numbers 0-9) and r = 2 (we're choosing two numbers for each domino).
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Applying the Formula: This gives us 10! / (2! * 8!) = (10 * 9) / (2 * 1) = 45. This represents the number of dominoes where the two numbers are different.
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Adding the Doubles: We also need to account for the dominoes where both numbers are the same (doublets): 0-0, 1-1, 2-2... 9-9. There are 10 such dominoes.
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The Final Count: Adding the dominoes with different numbers (45) and the doublets (10), we arrive at the total number of dominoes in a double-nine set: 45 + 10 = 55.
What About Other Domino Sets?
The same principle applies to other domino sets. For example:
- Double-six: This set would have (7 * 8)/2 + 7 = 28 dominoes.
This explanation clarifies not only the total number of dominoes but also the underlying mathematical logic. Understanding this allows you to calculate the number of dominoes in any double-N set.
Why are Double-Nine Sets Popular?
The double-nine set offers a good balance between complexity and gameplay. It's large enough to provide strategic depth but not so large as to become overly cumbersome.
Hopefully, this detailed explanation answers your question completely!
