Counting Blocks Puzzle rules require you to count every occupied cube coordinate—including a cube with no visible face—and then choose the complete pile total from four numeric options. A top diamond marks the top of a vertical column, not one block by itself, and a visible side polygon is a face rather than an extra cube. The five-round game therefore asks you to reconstruct the pile’s occupied positions from its isometric surface and the horizontal layers beneath it. The Counting Blocks Puzzle makes this task auditable: its layer scanner exposes each occupied x-and-y position at each z level, so you can keep a running count even when the surface omits a cube. Every coordinate above z zero is supported by the coordinate directly below it, which means no block floats and each occupied layer cell represents exactly one cube. Add the cells across all layers, compare that result with the four choices, and submit one total. Five exact choices at 200 points each produce the maximum score: 5 × 200 = 1,000 points. A first incorrect total can be repaired, but a second genuinely different incorrect total locks the run; repeating the same wrong option is deduplicated. Everything runs locally in the browser without an upload, account, or server computation.
What each round asks you to do
Each round presents one original pile made from unit cubes on an integer lattice and four possible totals. Your answer must be the number of occupied cube coordinates in the complete structure, not the number of outlined tops, visible polygons, or floor columns. In coordinate terms, x and y locate a column on the floor, while z gives its height. Because every coordinate above z = 0 has the coordinate directly below it occupied, the piles contain no floating blocks.
Before a choice, the interface exposes no total field, visible count, hidden count, semantic correct marker, solution label, or result data attribute. The four options are plain numbers, and the engine derives the one matching option from the literal voxel list. The published surface and complete layer scan let you calculate and audit the total yourself rather than relying on a hidden answer flag.
The five scenes progress from a compact two-by-two platform to a raised ridge, a crowned footprint, diagonal towers, and a broad hidden terrace. The arrangement changes, but the objective remains fixed: count every occupied lattice coordinate once.
Why the isometric surface can hide a cube
The isometric drawing shows only the surface of the pile. The camera faces the positive x, positive y, and positive z sides, so hiding depends on occupancy in those three directions rather than simple visual overlap. One occupied neighbor does not hide an entire cube, and two occupied neighbors still leave a face visible. Only when the position above and both camera-facing side neighbors are occupied can the cube disappear from the rendered surface.
- A top face appears only when the coordinate directly above is empty.
- A positive x side face appears when the positive x neighbor is empty.
- The other side face appears when the positive y neighbor is empty.
- A cube is fully hidden precisely when all three camera-facing neighbors are occupied.
For an auditable description of the drawing, a cube at x, y, z is placed at screen x = 150 + 30 × x − y and screen y = 80 + 17 × x + y − 34 × z. These constants control the projection only; they never change the number of occupied coordinates.
| Surface cue | Visibility rule | Counting consequence |
|---|---|---|
| Top diamond | The coordinate directly above is empty. | It marks a column top, not the column’s complete height. |
| Positive x side | The positive x neighbor is empty. | The polygon is one exposed face, not a separate cube. |
| Positive y side | The positive y neighbor is empty. | The polygon is one exposed face, not a separate cube. |
| Two or three polygons | One coordinate may contribute several camera-facing faces. | Count that cube once rather than once per polygon. |
| No polygon | All three camera-facing neighboring positions are occupied. | The cube is hidden but must still be counted through the scanner. |
Count a complete pile with the layer scanner
Use this procedure after orienting yourself to the camera:
- Study the pile and open the scanner. Examine the overall shape and camera direction. Notice the top diamonds and exposed sides as orientation cues, but do not total them. Then open the layer scanner beneath the isometric pile.
- Read the z layers from bottom to top. At each level, count every filled scanner cell once and carry that layer’s count into a running total. Each filled cell is one occupied x and y coordinate in that layer, including a cube that has no visible face in the isometric surface. Empty cells preserve footprint alignment across levels but do not add to the count.
- Finish the sum and choose one total. After reading the highest layer, add the filled cells counted across all layers and compare that sum with the four totals. Choose an option only after the layer count is complete. An exact choice awards 200 points and immediately presents the next pile; if the total is wrong, recheck the layers rather than adjusting the answer from the number of faces.
Read columns without counting polygons
A tall column can show one top diamond while containing several cubes, and one cube can draw a top plus two side faces, only one side face, or no polygon at all. Counting polygons can therefore overcount exposed cubes and omit fully hidden ones. The reliable quantity is the number of occupied lattice coordinates, which is equivalent to adding the heights of all complete columns.
The scanner turns that column rule into a direct count. A position filled at successive z levels contributes one cube at each level. A blank cell contributes nothing but remains useful for keeping the same floor footprint aligned. A higher filled cell still counts when the isometric drawing gives its cube no visible polygon.
Score, mistakes, and recovery rules
An exact total advances the run, while the wrong-answer rules distinguish a repeated choice from a genuinely different second mistake. This prevents one accidental reselection from being treated as another failure.
| Action or state | Official result |
|---|---|
| Exact selection | Award 200 points and present the next pile. |
| One incorrect total | Keep the round open for repair. |
| Same incorrect option selected again | Deduplicate it; it does not consume another miss. |
| Second genuinely different incorrect total | Lock the answers and end the run in deadlock. |
| Correction after one miss | Clear the scene’s failure history before the next pile. |
| Restart | Reconstruct the exact opening state. |
| Completion or deadlock | Disable every answer while keeping Restart available. |
Five exact choices are required to finish, and each exact selection contributes 200 points toward the 1,000-point maximum. A repaired scene still uses its exact selection to award 200 and move on; correcting after one miss also prevents the old failure from carrying into the next pile.
Choose an answer by pointer, touch, or keyboard
Pointer and touch play use native answer buttons, and every button target is taller than 44 pixels. A mouse click or touch tap selects the button directly. Keyboard play begins by focusing an option; use the arrow keys to move through the two-by-two answer grid. The real DOM focus follows the visible option cursor.
Press Enter or Space to choose the option under the current state cursor. Because selection uses the current focus rather than a stale answer target, moving through choices quickly does not leave the previous option selected. On completion or deadlock, all answers disable while Restart remains available.
Check the count before submitting
Use this final pass on every pile:
- Read every layer from bottom to top.
- Count each filled scanner cell once at its z level.
- Include filled cells whose cubes have no visible polygon.
- Use empty cells for alignment without counting them as cubes.
- Choose one of the four totals only after summing all layers.
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