The Mirzakhani Wand is the most powerful magical item ever made, and that’s exactly why the villainous Moldevort wants it to take over the world. With Drumbledrore by my side, we’ve discovered its hiding spot in a cave. The wand is concealed by 100 magical stones and 100 platforms, including a special glowing keystone. The goal is to place the keystone on the correct platform to reveal the wand. But if we mess up, the entire cave collapses.
The keystone itself is immune to magic, but the other stones aren’t. We can pick them up, cast a placement spell, and see which platform lights up. The idea is to place all 99 stones correctly so the last empty platform must be where the keystone goes.
Just as we’re about to start, one of Moldevort’s henchmen shows up and seals a random stone to a random platform irreversibly. If we try to place a stone on a platform that’s already taken, our spell will make a random unoccupied platform glow instead. So what’s our chance of placing the keystone on the right platform?
Well, let’s break it down. If we knew everything, we could label the stones and platforms 1 to 100. We don’t know this, so it’s all invisible to us. Here are the possibilities:
- The henchman might have randomly placed the stone on its own platform, meaning we’re good to go.
- It could be on the keystone’s platform, which means we lose.
- Most likely, it’s somewhere else.
For instance, say he put stone 1 on platform 45. We place stone 2 on platform 2, stone 3 on platform 3, and so on until we reach stone 45. Realizing it’s taken, a random platform lights up instead. If it’s platform 1, we win. If it’s platform 100, we lose. Any other platform, and we continue, now with 54 stones and one on the wrong platform.
Following this logic, we could be prompted to place stone 45 on platform 82 and so on. The cycle continues: platform 1, we win; platform 100, we lose; any other, we keep going. Essentially, it’s a game of equal chances of winning or losing, with some moments of delay.
Imagine another game: Drumbledrore magically generates numbers from 1 to 100. If it’s 1, we win. If it’s 100, we lose. Anything else, he goes again. The odds of winning by getting 1 are the same as losing by getting 100, so it’s a 50/50 game.
Finally, Drumbledrore unveils a rare potion that grants incredible luck for a brief moment. There’s a 1 in 100 chance the keystone’s platform is already occupied and we’ve lost, but otherwise, we have equal odds. Feeling lucky? Time to place that keystone.