12 Days of Christmas Gift Totals

1 minute read

Ever wonder how many gifts were given by “My True Love”? Let’s figure it out.

  • 1st day - 1 partridge
  • 2nd day - 2 turtle doves and 1 partridge -> total 3 new items this day.
  • Now the total is 1 + 3 = 4 -> (Day 1 plus Day 2)
  • 3rd day - 3 french hens, 2 turtle doves and 1 partridge - 6 items
  • New total is 4 + 6 = 10 items. Everything before this day gets repeated.

You can discover the grand total laboriously with a pen and paper, or you can write a formula: (This was written in php)

  • Let $n = number of days (12 days of Xmas and number of new gifts on the nth day)
  • Let $t = total gifts on previous day
  • Let $gt = grand total accumulated gifts.

Now go through the 12 days:

<?php
for ($n = 1; $n <= 12; $n++) //count up from 1 to 12
{
$t= $t + $n;  // t represents all the previous gifts, then add n gifts today
$gt += $t;  // accumulate all the yesterdays plus today for a grand total.
echo "Day $n Total = $gt <br>";
}
?>


Day 1 Total = 1
Day 2 Total = 4
Day 3 Total = 10
Day 4 Total = 20
Day 5 Total = 35
Day 6 Total = 56
Day 7 Total = 84
Day 8 Total = 120
Day 9 Total = 165
Day 10 Total = 220
Day 11 Total = 286
Day 12 Total = 364

Change $n to test other scenarios, such as n = 30 One month. Wow! If “True Love carried on for a month, the total would be 4960 gifts! and the song would be really irritating!”

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