How many gifts in the 12 days of christmas ?
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How many gifts in the 12 days of christmas ?
How many gifts are in the 12 days of christmas ?(The Twelve Days of Christmas)
Imagine you have a basket, and each day you're adding gifts to it.
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Day 1: You put 1 partridge.
- Total in the basket: 1
-
Day 2: You add 1 partridge and 2 turtle doves.
- Total in the basket: Previous total (1) + 1 + 2 = 4
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Day 3: You add 1 partridge, 2 turtle doves, and 3 French hens.
- Total in the basket: Previous total (4) + 1 + 2 + 3 = 10
This way, each day you're adding the previous day's gifts plus new ones.
To simplify the calculation, consider the following:
- Day 1: 1
- Day 2: 1 + 2 = 3
- Day 3: 1 + 2 + 3 = 6
- Day 4: 1 + 2 + 3 + 4 = 10
- Day 5: 1 + 2 + 3 + 4 + 5 = 15
- Day 6: 1 + 2 + 3 + 4 + 5 + 6 = 21
- Day 7: 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
- Day 8: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36
- Day 9: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
- Day 10: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
- Day 11: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 = 66
- Day 12: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 78
Adding up the totals for each day:
1 + 3 + 6 + 10 + ... + Day 12's total
It's like you're adding more and more gifts to the basket every day!
Now, for the final count, you add all these numbers together:
1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364
In total, the true love gave 364 gifts over the 12 days!
The formula for the total number of gifts given by day (n) is: [ T(n) = \frac{1}{6} n(n + 1)(n + 2) ]
This formula helps calculate the accumulated number of gifts up to any given day during the 12 days of Christmas.
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