Answer:
Approximately 2.97142857 × 10^27
Explanation:
To calculate how many decks you need to have one deck with each possible set of houses in KeyForge, you can use combinatorics. You mentioned that there are 7 possible houses, and each deck contains 3 different houses. We need to find out how many unique combinations of 3 houses can be chosen from the set of 7 houses.
This can be calculated using the combination formula:
C(n, k) = n! / (k! * (n - k)!)
Where:
C(n, k) represents the number of combinations of choosing k items from a set of n items.
n! represents the factorial of n, which is the product of all positive integers from 1 to n.
In this case, n = 7 (number of possible houses) and k = 3 (number of houses to choose for each deck).
So, the number of unique combinations of houses is:
C(7, 3) = 7! / (3! * (7 - 3)!)
C(7, 3) = 7! / (3! * 4!)
Now, calculate the factorials:
7! = 7 * 6 * 5 * 4!
3! = 3 * 2 * 1
Now, substitute these values back into the combination formula:
C(7, 3) = (7 * 6 * 5 * 4!) / ((3 * 2 * 1) * 4!)
Now, we can simplify:
C(7, 3) = (7 * 6 * 5) / (3 * 2 * 1)
C(7, 3) = (210) / (6)
C(7, 3) = 35
So, there are 35 unique combinations of houses for each deck.
Now, you mentioned that there are over 104,000,000,000,000,000,000,000,000 possible decks. To find out how many decks you need to have one deck with each possible set of houses, you divide the total number of decks by the number of unique combinations:
Total number of decks / Number of unique combinations = 104,000,000,000,000,000,000,000,000 / 35
Now, calculate this division:
Approximately 2.97142857 × 10^27
So, you would need approximately 2.97 x 10^27 decks to have one deck with each possible set of houses in KeyForge. This is an enormous number, illustrating just how vast the possibilities are in the game.