PAPER DECISION STUDIES
Sliding Tiles — Foundations: read the board before moving
Four starting positions, then four separate answer sheets. The IDs match the online studies.
This version uses a four-by-four grid containing tiles 1–15 and one blank. Only a tile directly above, below, left or right of the blank can slide into it. The goal is 1–15 in reading order with the blank at R4C4. There are no diagonal slides, edge wrapping or whole-row slides. The game creates its scrambles through legal moves from the goal.
Printing and using this pack
Use Print or Save as PDF. The first page contains instructions, the next four pages contain the tasks, and the remaining pages contain answers. An answer may continue onto another page. Check your print preview before choosing a page range. Print only the challenge pages if you want to keep answers separate.
Write a move and a reason before consulting the key. Rows count from the top and columns from the left. Four in a Row and Reversi diagrams state whose turn it is. The full online comparison includes all legal first moves; the answer sheets include the complete first-move comparison or a checked route.
CHALLENGE · slide-01
Find the adjacent tiles
Name every tile that can slide into the blank, then finish the board. A diagonal neighbour does not count.
My move or route: __________________________________________
My reason: ________________________________________________
________________________________________________________
CHALLENGE · slide-02
Read a central blank
Name every tile that can slide into the blank, then finish the board. A diagonal neighbour does not count.
My move or route: __________________________________________
My reason: ________________________________________________
________________________________________________________
CHALLENGE · slide-03
Make space before moving a tile
Plan the blank’s route before chasing a numbered tile. Compare the first moves, then find a shortest finish.
My move or route: __________________________________________
My reason: ________________________________________________
________________________________________________________
CHALLENGE · slide-04
Route around displaced tiles
Plan the blank’s route before chasing a numbered tile. Compare the first moves, then find a shortest finish.
My move or route: __________________________________________
My reason: ________________________________________________
________________________________________________________
ANSWER · slide-01
Find the adjacent tiles
The shortest finish takes 1 move. Initially movable tiles: 8, 12, 11. The distance comes from a complete breadth-first search outward from the target through 12 moves; it is not a general shortest-solution claim for arbitrary arcade shuffles.
Checked route
- Slide Tile 12 (R4C4) into the blank at R3C4.
ANSWER · slide-02
Read a central blank
The shortest finish takes 2 moves. Initially movable tiles: 7, 15, 10, 11. The distance comes from a complete breadth-first search outward from the target through 12 moves; it is not a general shortest-solution claim for arbitrary arcade shuffles.
Checked route
- Slide Tile 11 (R3C4) into the blank at R3C3.
- Slide Tile 12 (R4C4) into the blank at R3C4.
ANSWER · slide-03
Make space before moving a tile
The shortest finish takes 5 moves. A tile can travel only into the current blank. Use the complete route below to see which setup moves create that space. The distance comes from a complete breadth-first search outward from the target through 12 moves; it is not a general shortest-solution claim for arbitrary arcade shuffles.
Checked route
- Slide Tile 12 (R3C3) into the blank at R3C4.
- Slide Tile 11 (R3C2) into the blank at R3C3.
- Slide Tile 10 (R4C2) into the blank at R3C2.
- Slide Tile 14 (R4C3) into the blank at R4C2.
- Slide Tile 15 (R4C4) into the blank at R4C3.
ANSWER · slide-04
Route around displaced tiles
The shortest finish takes 7 moves. A tile can travel only into the current blank. Use the complete route below to see which setup moves create that space. The distance comes from a complete breadth-first search outward from the target through 12 moves; it is not a general shortest-solution claim for arbitrary arcade shuffles.
Checked route
- Slide Tile 9 (R2C2) into the blank at R3C2.
- Slide Tile 6 (R2C1) into the blank at R2C2.
- Slide Tile 5 (R3C1) into the blank at R2C1.
- Slide Tile 9 (R3C2) into the blank at R3C1.
- Slide Tile 10 (R4C2) into the blank at R3C2.
- Slide Tile 14 (R4C3) into the blank at R4C2.
- Slide Tile 15 (R4C4) into the blank at R4C3.