You arrive at the secret entrance to the North Pole base ready to start decorating. Unfortunately, the password seems to have been changed, so you can't get in. A document taped to the wall helpfully explains: "Due to new security protocols, the password is locked in the safe below. Please see the attached document for the new combination."

The safe has a dial with only an arrow on it; around the dial are the numbers 0 through 99 in order. As you turn the dial, it makes a small click noise as it reaches each number.

You're sure that's the right password, but the door won't open. You knock, but nobody answers. You build a snowman while you think.

As you're rolling the snowballs for your snowman, you find another security document that must have fallen into the snow:

"Due to newer security protocols, please use password method 0x434C49434B until further notice."

You get inside and take the elevator to its only other stop: the gift shop. "Thank you for visiting the North Pole!" gleefully exclaims a nearby sign. You aren't sure who is even allowed to visit the North Pole, but you know you can access the lobby through here, and from there you can access the rest of the North Pole base.

As you make your way through the surprisingly extensive selection, one of the clerks recognizes you and asks for your help. As it turns out, one of the younger Elves was playing on a gift shop computer and managed to add a whole bunch of invalid product IDs to their gift shop database! Surely, it would be no trouble for you to identify the invalid product IDs for them, right?

The clerk quickly discovers that there are still invalid IDs in the ranges in your list. Maybe the young Elf was doing other silly patterns as well?

You descend a short staircase, enter the surprisingly vast lobby, and are quickly cleared by the security checkpoint. When you get to the main elevators, however, you discover that each one has a red light above it: they're all offline. "Sorry about that," an Elf apologizes as she tinkers with a nearby control panel. "Some kind of electrical surge seems to have fried them. I'll try to get them online soon."

You explain your need to get further underground. "Well, you could at least take the escalator down to the printing department, not that you'd get much further than that without the elevators working. That is, you could if the escalator weren't also offline." "But, don't worry! It's not fried; it just needs power. Maybe you can get it running while I keep working on the elevators."

The escalator doesn't move. The Elf explains that it probably needs more joltage to overcome the static friction of the system and hits the big red "joltage limit safety override" button. You lose count of the number of times she needs to confirm "yes, I'm sure" and decorate the lobby a bit while you wait. Now, you need to make the largest joltage by turning on exactly twelve batteries within each bank.

You ride the escalator down to the printing department. They're clearly getting ready for Christmas; they have lots of large rolls of paper everywhere, and there's even a massive printer in the corner (to handle the really big print jobs).
Decorating here will be easy: they can make their own decorations. What you really need is a way to get further into the North Pole base while the elevators are offline.

"Actually, maybe we can help with that," one of the Elves replies when you ask for help. "We're pretty sure there's a cafeteria on the other side of the back wall. If we could break through the wall, you'd be able to keep moving. It's too bad all of our forklifts are so busy moving those big rolls of paper around."
If you can optimize the work the forklifts are doing, maybe they would have time to spare to break through the wall.

Now, the Elves just need help accessing as much of the paper as they can.
Once a roll of paper can be accessed by a forklift, it can be removed. Once a roll of paper is removed, the forklifts might be able to access more rolls of paper, which they might also be able to remove. How many total rolls of paper could the Elves remove if they keep repeating this process?

As the forklifts break through the wall, the Elves are delighted to discover that there was a cafeteria on the other side after all.
You can hear a commotion coming from the kitchen. "At this rate, we won't have any time left to put the wreaths up in the dining hall!" Resolute in your quest, you investigate.

"If only we hadn't switched to the new inventory management system right before Christmas!" another Elf exclaims. You ask what's going on.
The Elves in the kitchen explain the situation: because of their complicated new inventory management system, they can't figure out which of their ingredients are fresh and which are spoiled. When you ask how it works, they give you a copy of their database.

The Elves start bringing their spoiled inventory to the trash chute at the back of the kitchen.
So that they can stop bugging you when they get new inventory, the Elves would like to know all of the IDs that the fresh ingredient ID ranges consider to be fresh. An ingredient ID is still considered fresh if it is in any range

After helping the Elves in the kitchen, you were taking a break and helping them re-enact a movie scene when you over-enthusiastically jumped into the garbage chute!

A brief fall later, you find yourself in a garbage smasher. Unfortunately, the door's been magnetically sealed. While you're trying to figure out how to escape, you are approached by a family of cephalopods! They're pretty sure they can get the door open, but it will take some time.

While you wait, the youngest cephalopod asks for your help with their math assignment. The problems are arranged in a visual puzzle format - columns of numbers with operators at the bottom.

After thanking your cephalopod friends, you escape the trash compactor and find yourself in the familiar halls of a North Pole research wing. You discover a facility labeled "teleporter hub" and step onto a large yellow teleporter pad.

You're transported to an unfamiliar room! The room has no doors; the only way out is the teleporter. Unfortunately, the teleporter seems to be leaking magic smoke. Using the diagnostic equipment, you identify error code 0H-N0, indicating an issue with one of the tachyon manifolds.

You locate a diagram of the malfunctioning device and must analyze how tachyon beams interact with it to understand the beam-splitting properties of the tachyon manifold and repair the teleporter system.

The teleporter brings you to an underground space containing a giant playground. A group of Elves are constructing an elaborate Christmas decoration project involving suspended electrical junction boxes.

The Elves need to connect these junction boxes with strings of lights so that electricity can reach every location. But they have limited materials: "To save on string lights, the Elves would like to focus on connecting pairs of junction boxes that are as close together as possible."

They want to understand how their final circuit configuration will look, particularly regarding the sizes of the resulting connected groups.

You slide down a firepole in a corner of the playground and arrive at the North Pole base movie theater!

The Elves are redecorating the theater by replacing tiles in a grid floor pattern. Some tiles are red, and the Elves need to identify the largest possible rectangle using red tiles as opposite corners.

You receive a list of red tile coordinates and must calculate which two tiles form a rectangle with maximum area.

You arrive at a large factory where the Elves are unable to operate the machines: "the factory machines are all offline, and none of the Elves can figure out the initialization procedure."

The comedic twist: the instruction manual's section detailing the initialization procedure was eaten by a Shiba Inu! What remains are only partial technical documents - indicator light diagrams, button schematics, and power specifications.

Your task is to decipher how to properly configure the machines' indicator lights using the available documentation fragments.

You hear loud beeping coming from a hatch in the floor of the factory. Descending the ladder, you discover a large toroidal reactor powering the facility above.

An Elf urgently explains: "We just installed a new server rack, but we aren't having any luck getting the reactor to communicate with it!" The team believes the issue is triggered by data following some specific path through the devices.

Your task is to trace every path from you to out - starting at a device an Elf hastily labeled "you" and ending at "out," the main reactor output.

Racing against time, you discover a ventilation duct that leads to a large, well-lit cavern full of Christmas trees. A group of Elves are working frantically to decorate before the deadline.

They face one significant worry: "the presents for all the young Elves that live here at the North Pole." It's an ancient tradition to put the presents under the trees, but the Elves are worried they won't fit.

The presents come in various unusual shapes and must be placed on a two-dimensional grid - they can be rotated and flipped, but cannot overlap or stack. Can you help fit them all?