Pokémon Friends has more than forty types of puzzles, each with several difficulty levels. They are played in series of three: the better you do, the nicer the ball of yarn you earn. Here is the list, based on Serebii; the titles are those of the English version, and the last column shows the content that unlocks them.

Pokémon Friends.
PuzzleGoalContent
Pikachu’s Power LineConnect all the light bulbs in a single lineFree
Sableye’s Twisty TracksAssemble the rails to reach the finishFree
Pansage and Pals CaféAre the numbers on both sides equal?Base Pack
Makuhita’s Mighty MovesPush the boulders to reach the finishBase Pack
Think Outside the BoxRotate the box to free the PokémonFree
Leapin’ LittenClimb the levels to the finishFree
Find the Froakie!How many Froakie are there?Base Pack
Last Balloon LeftPick the balloon that won’t popBase Pack
Greninja’s Secret ShapesWhich shape will the cutout make?—
Lotad’s Ferry ServiceTravel on Lotad to the finishBase Pack
Spheal SpinnerRoll Spheal to the finishFree
Pumpkaboo’s Shadow ShowWhat shape will the shadow have?Base Pack
Tinkatuff TunnelingBreak the rocks to reach the finishPuzzle On! 1
Morpeko MedalsCircle the medals to turn them yellowPuzzle On! 1
Flight PathsRotate the Pokémon to avoid a collisionBase Pack
Who Goes Where?Fill the empty spots based on the photosPuzzle On! 2
How Many More?How many more Pikachu are there?Puzzle On! 1
Smeargle’s Picky PalettePaint without letting two identical colors touchPuzzle On! 1
Medal MatchBring the medals to their placesBase Pack
Secret StoneFill in the holes to complete the pictureBase Pack
Don’t Wake Gengar!Light up the corridors without waking GengarPuzzle On! 2
Square SolverForm the perfect squarePuzzle On! 1
Klefki’s KeysOpen the doors to reach the finishBase Pack
Blocked BoxesHow many boxes are hidden?Puzzle On! 2
Operation: Bath TimeFlood the area to wash away all the dirtPuzzle On! 1
Shine on CherrimGet the light to CherrimBase Pack
Topsy-Turvy EspeonFlip gravity to reach the finishPuzzle On! 2
Take It for a Spin!What will the object look like as it turns?Base Pack
Yamper the ChampTake the shortest pathPuzzle On! 1
Dig, Drilbur, Dig!Connect the tunnels to collect all the mushroomsBase Pack
Tidy Toxel’s ToysPut all the blocks away in the boxBase Pack
Minccino’s Clean SweepClean in the right order up to the trash can—
Stamp-n-RollWhere will the stamp leave its mark?Puzzle On! 2
Count on GimmighoulFill in the missing numbers in orderBase Pack
Bricks and LaddersBreak the walls to reach the finishPuzzle On! 2
Don’t Slip Up, PiplupSlide across the ice to the finish—
Porygon’s LabWhich 3D shape is in the box?Puzzle On! 2
Perfect FitChoose the block that fills the spaceFree
Squirtle the GardenerDraw a path for the waterBase Pack