Merry Hanukka/Kwanzaa/Christmas!
There is frantic activity in Santa's North Pole Workshop these last few days before Christmas. Or perhaps Santa's North Pole Logistics Hub is a better description, as several years have passed since the last toy was actually manufactured there. All toys are now imported from another entity (who's name happens to be an anagram of "Santa"), and are only rebranded and repackaged at the former workshop to hide their origin.
In order to not have to handle a huge list of item ID numbers for all the rebranded toys (the Non-documented AUgmented GHosting, Test/evaluation and Intrusive surveillance summary list, a.k.a "Santa's NAUGHTI List", is long enough), Santa has decided to calculate the ID numbers on the fly using the item IDs from the vendor catalogue. His super-secret algorithm works as follows: the original ID is multiplied by a number and then another number is subtracted from the resulting product until another operation would result in a negative number. The exact numbers are only known to Santa himself, the only details known to the elves are that the first number is smaller than the second, the second number is larger than the sum of the numbers in the vendor catalog, and the numbers are coprime.
According to some rumors, there is also a third secret number related to the other two, and this third number can be used to recreate the original vendor ID number if needed, for example in case of any warranty claims.
To raise the elves's stress levels even higher, one trailer carrying knapsacks (i.e. shipping containers) tipped over while in transit to the sled loading bay. Except some minor dents and scratches, most of the knapsacks appear to be more or less undamaged.
One of them, however, broke its display and is no longer showing any destination coordinates. A closer inspection revealed the entire shipping manifest to be damaged; the field labeled "weight" reads "222501594353295949169399528", which is a number several orders of magnitude larger than what would be expected, and the list of contents is completely scrambled with only one readable line, "178437364998980288322326970", and the rest being only those special characters no one ever uses.
It would be very time-consuming to move the knapsack to the side, open and empty it, go through all the contents, find a matching manifest, and finally load the knapsack again. In an attempt to unveil the knapsack's destination faster, the elves have found a list of items delivered to the loading station the knapsack came from; might it be possible to use that to find the missing coordinates? If not, the delivery of the contents of this knapsack might be delayed to after New Year's...
Item ID Description
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04993-67269-28190-34020-18444 Pet rock
05209-75188-88202-04910-03736 Flashlight
07854-07846-09331-76097-84065 Necklace
08334-16359-19852-89328-39994 Screwdriver
08809-30895-44273-93880-30537 Elf figurine
09074-86580-83557-30277-74890 Wooden building blocks
09308-05656-60405-19833-56552 GPS
13307-23850-28324-37893-24656 Kaleidoscope
13406-64215-85812-73298-05997 My little pony
17098-63235-37515-91767-94284 Pop-up book
18010-72990-39618-56161-20884 Dreidel
18984-09153-94377-07007-33953 Socks
19129-43813-68509-86268-33065 Octopus plushy
19603-92707-10261-69581-40759 Baseball bat
20144-94786-34319-78863-62218 String, 1m
21969-81632-10662-81221-36972 Yo-yo
24238-75475-53668-99049-39061 Teddy bear
24496-35382-40775-51336-21851 Xylophone
25924-09592-16939-77976-53821 Slinky
25928-13124-77860-95959-18716 Yahtzee
32129-05858-52480-51944-39292 Marbles
32495-15013-00155-86061-55479 Jack-in-the-box
32542-08224-30420-76820-59255 Pogo stick
34815-63649-20074-14389-99507 Spirograph
36427-59647-55659-08681-08843 Zergling plushy
39112-00769-00109-02964-11564 Viewmaster
39460-83890-18950-36894-90879 Dominoes
40044-01508-72286-65747-19652 Magnet
41627-32757-01353-67887-03094 Vampire teeth
42132-39610-83612-45702-37804 Jigsaw puzzle
42222-23557-69399-22798-75499 Quadcopter
45014-47618-87352-17768-91870 Matchbox
45266-95321-42239-38123-13170 Boomerang
47747-41791-94859-76523-56029 Pac-man arcade game
47907-60674-03649-30703-48125 Unicorn
48505-61277-40214-90182-64755 Rubber ducky
50407-63882-01360-46763-40899 Lucky 8-ball
50664-96543-49090-84286-28997 Charcoal lump
54887-78048-51439-94584-14813 Inflatable castle
55149-00496-13808-55147-90957 Glowstick
56062-97765-55942-30449-44824 Crayons
57147-83555-37908-71574-08378 Etch-a-scetch
57473-29627-20986-63083-38584 Action figure, "Toa Norik"
62089-05355-47959-77421-83921 Hungry hungry hippos
62492-39175-74835-32084-02705 Rocking horse
62591-80770-14668-07910-14081 Tamagochi
64268-05249-29311-87036-00468 Wall clock
64694-59045-81870-53625-29709 Candy
71062-19672-77189-97224-28746 Balloon animal kit
75282-22757-38508-79737-75300 Hockey puck
76079-91221-07204-67424-61360 Football
78708-37533-94487-66357-78205 Pencil
79613-70063-05036-77110-28695 Matryoshka
79767-49069-08963-44910-30236 Hoverboard
80035-59976-31644-62150-71095 Kite
83200-22142-20042-03557-29234 Radio-controlled car
85020-37013-06582-77503-29973 Shoe laces
85846-09442-44976-45582-88775 Wooden train set
86209-94440-81479-94625-07876 Ant farm
92222-28013-29012-99832-15485 Fidget spinner
92462-81799-90933-62252-20312 Frisbee
93305-51134-24282-26032-78878 Water gun
93535-14070-63974-96270-86276 Rubik's cube
start with the left checker below:
