Calculating Gift Counts for "The Twelve Days of Christmas": Looping Edition

In yesterday's article, I posted a reader challenge:

How many total gifts does one's true love deliver by the nth day of Christmas?

SPOILER ALERT: If you would like to try figuring it out on your own, follow the link above to read the original article before scrolling down to see one of my solutions.

The goal is to write a function that takes as input the first column (Day of Christmas) and returns as output the last column (Cumulative gifts):

Using a Loop to Calculate the Total

This solution is based on the following pattern that emerges when one studies the above matrix:

1: (1 × 1)
2: (1 × 2) + (2 × 1)
3: (1 × 3) + (2 × 2) + (3 × 1)
4: (1 × 4) + (2 × 3) + (3 × 2) + (4 × 1)
5: (1 × 5) + (2 × 4) + (3 × 3) + (4 × 2) + (5 × 1)
6: (1 × 6) + (2 × 5) + (3 × 4) + (4 × 3) + (5 × 2) + (6 × 1)

If you notice, the first number in each multiplication couplet increments from 1 to n and the second number in each couplet decrements from n to 1.

Based on the above pattern, the solution below goes through a loop n times and accumulates the total number of gifts given up to and including on day n.

'--== Looping Version ==--
Function GiftsByXmasDay(DayOfXmas As Long) As Long
    
    'Initialize x and y
    Dim x As Long: x = DayOfXmas
    Dim y As Long: y = 1
    
    Dim i As Integer
    For i = 1 To DayOfXmas
        GiftsByXmasDay = GiftsByXmasDay + x * y
        x = x - 1  'Decrement x
        y = y + 1  'Increment y
    Next i
End Function

Referenced articles

Reader Challenge: Write a Formula to Calculate Gift Totals in “The Twelve Days of Christmas”

How many total gifts does one’s true love deliver by the nth day of Christmas? It’s a deceptively tricky problem to solve.

No Longer SetMike Wolfe

Cover image created with Microsoft Designer