You are stuck in a room with 100 floor tiles, and a magic button which you can carry with you. There are three types of tiles: real, fake and nopey. There are at most 49 fake tiles, and there is at least one real tile. To give a clue on the types of some tiles, you can stand on one tile and press the magic button, then stand on another tile and press the magic button again. That counts as one move. Moves are not subdivided up further.
After that, the following will happen.
- If the first tile is real, you will hear a beep if the second tile is fake, else nothing.
- If the first tile is fake, you will hear either a beep or nothing randomly, with a 50% chance of either, no matter what the second tile is.
- If the first tile is nopey, you will hear nothing, no matter what the second tile is.
Your goal is to find a tile that is not fake. If you find one, you can jump on that tile three times. If it is not fake, you can leave the room. But if it is fake, you will be stuck in the room forever.
Question: How can you successfully find a non-fake tile (real or nopey), in as few moves as possible?