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.

1. Day 1: You put 1 partridge.

   • Total in the basket: 1

2. Day 2: You add 1 partridge and 2 turtle doves.

   • Total in the basket: Previous total (1) + 1 + 2 = 4

3. 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.