What to do with Mysterious Slates
Mysterious Slates are collected purely to slot into a hidden Unown wall puzzle in Withered Wasteland, and completing it rewards Mew.
Mysterious Slates aren't used in any recipe — their only purpose is the Mysterious Mural, a hidden puzzle room. Each slate shows an abstract pattern on the front and an Unown symbol on the back; you find them as one of several possible rewards (alongside fossils, relics, and CDs) when breaking glowing dig spots with Rock Smash, so pulling a slate on any given day comes down to chance rather than a guaranteed drop.
To reach the mural, head to the Withered Wasteland Pokémon Center, then go behind and slightly right of the building. Break the wall block you find there and clear the rubble behind it to reveal a stairway down to a chamber lined with an Unown-shaped socket for every letter of the alphabet. Placing a slate into the wall automatically matches it to its Unown symbol — hold a slate or set it on the ground to check which letter is on the back if you'd rather sort them by hand first.
Sources differ on the exact total: some counts land on 27 slates (A through Z, plus one bonus "!?" slate), others put the full set at 28. Either way, filling the entire wall is what unlocks the reward — Mew joins your town as a resident Pokémon. The game won't hand you a duplicate slate until you've collected every unique one, and slates keep dropping after the puzzle is solved, so extras become spare trade goods for other Pokémon.
Regions: Withered Wasteland
Slate count is uncertain — sources report both 27 and 28 total slates.