Day 19: The Lunar Refinery
Previously
On the Isle of Shifting Shadows, you solved the ancient sundial puzzle, carefully aligning the shadow to reveal the hidden passcode. With each precise rotation, you unlocked the next fragment of the Veil of Wonder. Now, as the shadows recede and the island returns to its calm, you set your sights on the next destination in your quest to restore Christmas magic.Narrative
The Island of Twisted Toys is a haunting blend of wonder and distortion, where towering, oversized toys lie abandoned under a dim, flickering sky. Cracked doll faces peer out from piles of gears, and rusty merry-go-round horses creak in the wind. As you venture deeper into the island, you sense a faint magical energy pulsing from a structure ahead — a massive, strange contraption that looms over the ruins of an old carnival attraction.
This is the Mystic Processing Wheel, a legendary device once used to refine Lunar Dust — a material so potent it powers the island’s enchanted toys. As you study the wheel’s intricate engravings, the faded voice of the Guardian echoes faintly in your mind.
"The Mystic Processing Wheel holds great power," she whispers. “Only by refining enough Lunar Dust will you unlock the energy to release the next fragment of the Veil of Wonder. But take caution — the wheel’s enchantment is ancient and follows a precise rhythm.”
The wheel has 10 compartments, each capable of holding two measures of Lunar Dust. As it spins, dust is loaded into each compartment at the bottom, and each compartment rises to a Processing Chamber at the top, where the dust is refined before being released back at the bottom. With only 30 minutes allocated for this island, you carefully begin loading Lunar Dust, aiming to maximize the amount refined before time runs out.
Objective
Calculate the maximum amount of refined Lunar Dust that you will have available within the 30-minute window.
Challenge
Challenge
On the Mystic Processing Wheel, you have 10 compartments for refining Lunar Dust. Each compartment can hold two measures of dust and rotates so that one compartment rotates through the exit platform every minute, passing through the Processing Chamber at the top before releasing the refined dust at the bottom.
The wheel has been activated, and you have exactly 30 minutes to maximize the amount of Lunar Dust refined before the window closes. Dust can only be added to compartments at the bottom of the wheel, and it takes one minute for each compartment to advance to the position where the next compartment was.
Calculate the maximum amount of Lunar Dust you can refine in this time.
Hint 1
Think about the way the wheel works. If two measures are added at the bottom compartment, how much time will pass before they return?Hint 2
If you only have 30 minutes, that means that at some point it will not be worth to add more Dust, as there will be no time for it to return.Answer
Wrong answer!Outcome
As the Mystic Processing Wheel completes its final cycle, the refined Lunar Dust gathers in a small basin at the base of the wheel. You scoop up the shimmering dust, feeling its magical energy tingling against your fingers. Carefully following the faint instructions left by the Guardian, you sprinkle the dust onto an intricate, rune-inscribed lock on a nearby pedestal.The dust glows as it settles into the grooves, activating the lock with a soft hum. Suddenly, the lock clicks open, and a hidden compartment reveals itself, containing the next fragment of the Veil of Wonder. With the fragment in hand, you feel the island’s magic calm as you prepare to move on, another step closer to restoring the Veil.