Shadow Stack: A Spatial Reasoning Game Where Every Block Casts Two Shadows
There is a pole, a tray of toy blocks, and two walls with a gray shadow on each. Thread blocks onto the pole, bottom to top, until the stack casts exactly those two shadows. That is all of Shadow Stack, and it is harder than it sounds, because a block doesn't have one shape so much as two: a disc is a circle from the front and a thin bar from the side, and which is which depends on how you turn it.
Puzzles like this get called a 3D shadow puzzle, shadow building blocks, or a spatial reasoning game. Spatial reasoning is the knack of holding a solid object in your head and knowing what it looks like from somewhere else, and this is about as pure an exercise of it as there is. It is also the "front view and side view of a 3D shape" question from school geometry, turned into a toy you can spin.
📏 The Rules, All of Them
- The gray shape on each wall is the shadow to build. The right-hand wall shows the stack from the front; the left-hand wall shows it from the side.
- Pick a block from the tray. It hovers over the pole and casts a blue preview shadow on both walls, where it would land.
- Spin turns the block a quarter turn around the pole. Tip rolls it a quarter turn onto its side.
- Drop it. A layer that matches turns dark on that wall; one that doesn't turns red.
- Blocks stack from the bottom up, and only the top block can come off, as on a real pole.
- The tray always holds more blocks than the answer needs. The extras are decoys.
- You win when your stack's shadow matches the gray shape on both walls. Any stack that does it counts.
🔦 Front View, Side View: What the Two Walls Show
The shadows here fall straight back, so nothing stretches: a block two squares wide casts a shadow two squares wide, on either wall, wherever it sits on the pole. That makes each wall a true flat picture of the stack from one direction, what a drafter calls the front view and the side view. School geometry usually adds a third, the top view; this game works with two.
🧩 Two Shadows Pin a Shape
One shadow tells you surprisingly little. Two, read together, usually name the block. Every row of this table is true of the blocks on this page, whichever wall each shadow lands on:
| One wall | The other | The block |
|---|---|---|
| Ball | ||
| Disc, standing on its edge | ||
| Cylinder, lying on its side | ||
| Cone, tipped onto its side | ||
| Cone or pyramid (identical standing up) | ||
| Triangle block | ||
| Cube, or a cylinder standing on end | ||
| Pyramid, tipped onto its side | ||
| Dome | ||
| Half disc |
🕵️ Look-Alikes: Check the Second Wall, Then Count the Squares
There are 25 different blocks, and they were chosen to overlap. Five of them can cast the small circle: the ball, the small disc, the cylinder, the small dome and the cone. Five more cast the big circle, and three cast the very same triangle. So a blue preview that sits perfectly inside one gray shape proves nothing until you have looked at the other wall, where the ball is still a circle, the disc has become a bar and the cone is a triangle lying on its side.
Every Medium and Hard puzzle is built so that at least two of its layers have a look-alike waiting in the tray: a block that matches that layer on one wall and not on the other. Measured over 300 puzzles of each, the real figure is higher, about 4.3 of Medium's five layers and 5.4 of Hard's six.
Size is the other half. The walls carry a grid, and several blocks come in two sizes: a small disc two squares across and a big one three across, a cone and a wide cone, a ball and a big ball, a dome and a small dome. The tray draws every block to the same scale, so when two candidates have the right outline, count the squares the gray shape covers.
🔄 Spin and Tip
A cube looks the same however it sits. A brick can cast six different pairs of shadows, and the half disc, the trapezoid, the low roof and the wide triangle block can each cast ten. Across all 25 blocks there are 128 distinct pairs, and Spin and Tip are how you move between them: from any position, any other is at most five presses away, and usually one or two. Watch the blue preview while you press. It turns with the block, on both walls at once.
Upside down counts. A cone standing on its point casts a triangle pointing down, and a dome flipped over becomes a bowl. Both turn up in puzzles, and two Tips flip a block over.
🪤 Hard Mode: the Block That Fits but Belongs Higher Up
Some different blocks cast identical shadows on both walls. A cube and a cylinder standing on end are the same two squares. A cone and a pyramid are the same two triangles. A small disc lying flat, a square tile and a triangle block laid flat are all the same low slab. There are 14 such pairs among the 25 blocks.
Every Hard puzzle hides at least one trap built from a pair like that: a layer that two blocks in your tray can both make, and a layer above it that only one of the two can make. Use the wrong one low down and everything keeps matching, dark shadows on both walls, until you reach a layer nothing left in the tray can build.
A player who simply drops any block that fits finishes every Easy and every Medium puzzle we generated, and only 43% of Hard ones. When that player does get stuck there are, on average, about four blocks on the pole and two of them have to come back off; half the time it is only the top one.
⚠️ Three Ways It Goes Wrong
- Matching one wall. The preview fits on the right and you drop without glancing left. This is the mistake the decoys are there to catch.
- Reading a tall shape as one block. Medium and Hard have no layer lines, and neighbors often run together: in two Medium puzzles out of three, and five Hard ones out of six, some pair of neighboring blocks meets on one wall with no visible seam. The other wall usually gives the join away.
- Building on a red shadow. Only the top block comes off, so a wrong layer low in the stack means unstacking everything above it. Check each drop before the next.
🎚️ What Easy, Medium and Hard Mean on This Page
Every puzzle is generated when you ask for it, and each level is a set of promises the generator checks before it shows you anything. The last row was measured over 300 puzzles per level by a checker written separately from the generator.
| Easy | Medium | Hard | |
|---|---|---|---|
| Blocks in the answer | 3 | 5 | 6 |
| Decoys in the tray | 2 | 3 | 4 |
| Blocks it draws from | 15 simpler shapes | All 25 | All 25 |
| Layer lines on the walls | Yes | No | No |
| Presses an answer block starts from its place | 0 or 1 | 1 or 2 | 1 or 2 |
| Can a block that fits both walls be the wrong one? | Never | Never | Yes, at least once |
| Puzzles with exactly one way to build them | 92% | 81% | 71% |
A ball or a cube looks the same every way up, so those start with nothing to turn.
We don't promise a single answer, and the last row is why: a shadow cannot tell a cube from a cylinder on end, so when both are in the tray either one wins. Everything else in the table is checked on every puzzle before you see it.
🎮 Playing on This Page
Tap a block in the tray to pick it up, and tap it again to put it back. Take Off lifts the top block back into your hand. Tapping the scene itself drops the block you are holding, or lifts the top one if your hand is empty. On a keyboard the left and right arrows choose a block, S spins, T tips, the down arrow drops and the up arrow takes off.
Hint puts the next block in your hand, already turned the right way; if the pole can't be finished as it stands, it takes the top block off instead and says why. Solution builds a complete answer. Finish with no hints and without ever taking a block back off, and the page calls it a perfect build.
📜 Where Shadow Puzzles Come From
The idea that two flat views at right angles pin down a solid is older than any toy. Gaspard Monge built a whole method of drawing on it, published in 1799 as Géométrie descriptive. The playful version appeared on the cover of Douglas Hofstadter's Gödel, Escher, Bach in 1979: blocks he carved himself so that their shadows in three directions spell G, E and B. As a toy, stacking blocks on pegs to match an outline is the idea behind SmartGames' Day & Night, designed by Raf Peeters and released in 2009, where half the challenges show only silhouettes. The wooden set that prompted this page is the game above made real: one peg, a handful of blocks, and a booklet standing open at a right angle with a shadow on each page. None of these are shadow matching games, where you pair a picture with its outline and there is nothing to turn.
🧒 Spatial Reasoning Without the Worksheet
"Draw the front and side view of this solid" is a standard geometry exercise, and most children meet it on paper. This is the same question asked backward, with a toy: here are the two views, now build the solid. A child who can tell a circle from a triangle can play Easy, where the layer lines show how many blocks there are, no block starts more than one press from its place, and it is impossible to build yourself into a corner. Hard asks for something adults find hard too: holding back a block that fits, because you can see where it will be needed.
So start at the bottom, read one layer across both walls, count the squares, and never trust a single shadow. When a cone you were sure about turns out to be a pyramid, you'll see why this one is worth a second go. 🔦