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Use Linear Equations to solve this unique 12 days of Christmas Problem
In order to express his true love to his lady, a liege decided to present her with a genuine 12 days of Christmas extravaganza.
Unfortunately, he was not the brightest and had trouble remembering what to purchase.
Now just keep in mind when attempting to solve this puzzle, that any time something is sold, killed, or otherwise discarded we will assume that the lord gets his money back on that particular purchase.
As such, he encountered a few pitfalls along the way. His adventures proceeded as follows:
On the first day of Christmas the lord purchased 1 Partridge in a Pear Tree, 6 Turtle Doves, 3 French Hens, 1 Geese a Laying, 8 Maids a Milking, 2 Lords a Leaping and 4 Drummers Drumming. He paid out $2023.24 for his purchases.
On the second day of Christmas the lord purchased 2 Calling Birds, 5 Gold Rings, 1 Lord a Leaping, 7 Pipers Piping and 3 Drummers Drumming. One of the French Hens was consumed for dinner and two of the Maids a milking got into a fight and were fired. (This is the only time I’ll repeat that the Lord receives a refund if anything dies, is sold, discarded, returned etc…) He paid out $2805.08 for his purchased (this factors in a credit for items refunded, discarded, returned, dead, etc…)
On the third day of Christmas the Lord purchased 2 Geese a Laying and 2 Swans a swimming. He determined that the partridge in the pear tree was not good enough for his fair love, 5 turtle doves flew the coop, a French hen was again consumed for dinner and 2 of the Drummers Drumming were fired because they did not possess their own drums. The lord, despite the credits, paid out $606.58 today.
On the Forth day of Christmas, the Lord purchased 2 Partridges in a Pear Tree, 1 Calling Bird, 1 Swan a Swimming, 2 Pipers Piping and 1 Drummer Drumming. He AGAIN, consumed a French hen for dinner. It turned out that the Gold Rings were not pure gold so he returned all 5, 2 of the Maids of Milking had a disease of the hands and were let go and 1 Lord of Leaping decided to leave with the Maids. The Lord paid out $676.12 today.
On the Fifth day of Christmas the Lord purchased 2 Turtle Doves, 2 French Hens, 1 Gold Ring and hired 3 Lords a Leaping and 7 Drummers Drumming. A Calling Bird and a Swan a swimming each died of the avian flu and 5 pipers piping disappeared never to be heard from again. The lord spent $1045.93 today.
On the Sixth day of Christmas the Lord purchased 1 Geese a Laying, 2 Swans a Swimming and he hired 1 Lord a Leaping. 3 of the Turtle doves had an unfortunate accident during a magic show, 1 French Hen was served as dinner yet again while 2 calling birds were returned for their inability to fly, and 2 Maids a Milking and 6 Drummers Drumming were let go because of their inability to keep their hands to themselves. The Lord paid out $173.66 today.
On the Seventh Day of Christmas 1 Turtle Dove, 1 Calling Bird, 1 Gold Ring, 2 Swans a Swimming were purchased and 3 Pipers Piping and 3 Drummers Drumming were hired.
1 French Hen was served up for dinner and 2 lords a leaping were fired because they just couldn’t leap high enough. The lord paid out $1709.15.
On the Eighth Day of Christmas the Lord, in great insight towards his past tendencies, purchased 7 French Hens. He also bought and paid for 4 Calling Birds 2 Pipers Piping and 2 Drummers Drumming. He returned both Partridges in a Pear Tree because they were inseparable, 1 Geese of Laying was murdered by some local children, and 2 Maids a Milking were fired for skimming the cream off of the milk. The lord paid out $999.30.
On the Ninth Day of Christmas the Lord Purchased 1 Turtle Dove, 1 Gold Ring, 2 Geese a Laying, and hired 10 Ladies Dancing and 1 Lord a Leaping. He consumed 1 French Hen for dinner, lost 3 Swans a Swimming when his pond froze over and lost one Drummer Drumming to food poisoning. His daily spending amounted to $3649.79.
On the Tenth Day of Christmas the Lord purchased 1 Gold Ring, 1 Swan a Swimming and Hired 2 Lords a Leaping, 1 Piper Piping and 1 Drummer Drumming. As if there was ever any doubt, he consumed 1 French Hen for dinner, while returning 1 turtle dove and 1 calling bird. He spent $1682.73
On the Eleventh Day of Christmas the Lord purchased 1 Partridge in a Pear Tree, 1 Calling Bird, 1 Gold Ring, 1 Geese a Laying and 1 Piper Piping. He consumed 1 French Hen for dinner and fired 1 Drummer Drumming for oogling his true love. He spent $311.29.
On the Twelfth day of Christmas the Lord purchased 1 Turtle Dove, 3 Swans a Swimming, 8 Maids a Milking, 3 Lords a Leaping and 1 Drummer Drumming. He again consumed a French Hen for dinner (isn’t he tired of them yet?) returned a calling bird, and had to let 1 lady dancing go because he realized that he hired too many. He spent $2637.62
Although the following has no impact on your solution, the lord ultimately did in fact have 1 Partridge in a Pear Tree, 2 Turtle Doves, 3 French Hens, 4 Calling Birds, 5 Gold Rings, 6 Geese a Laying, 7 Swans a Swimming, 8 Maids a Milking, 9 Ladies Dancing, 10 Lords a Leaping, 11 Pipers Piping and 12 Drummers Drumming for a total cost of $18320.49.
Allow the following variables to represent the cost of one of item.
A = 1 Partridge in a Pear Tree – 3 Turtle Doves + 16
B = (1 Calling Bird + $0.01)/2 – 50
C = 2 Gold Rings – 3 Geese a Laying + 3
D = 1 Maid a Milking – 4.55
E = 1 Lady Dancing – 1 Lord a Leaping – 103
F = 1 French Hen - 10
Coordinates
N 39 36.ABC
W 077 47.DEF
Additional Hints
(Decrypt)
Pyhr: Jevgr n flfgrz bs rdhngvbaf naq fvzcyvsl gur flfgrz va ebj erqhprq rfpuryba sbez (EERS) naq nyy jvyy or erirnyrq.