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Lizely

Counting Blocks Puzzle

Count complete isometric cube piles by reconstructing vertical columns and including blocks hidden behind visible faces.

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How to use

  1. 1.Study the isometric pile to understand its overall shape and camera direction, then open the layer scanner beneath it.
  2. 2.Read the z layers from bottom to top. Every filled scanner cell is one occupied x and y coordinate, including cubes hidden in the isometric surface.
  3. 3.Count the filled cells across all layers and choose one of four totals. Five exact choices at 200 points each produce the maximum score.

About Counting Blocks Puzzle

Counting Blocks Puzzle is a five-round visual reconstruction game about unit cubes arranged on an integer lattice. Each round shows one original isometric pile and four possible totals. The visible drawing is only the surface of the structure. Some cubes have no face visible from the selected camera direction, but they still occupy positions inside supported columns and must be included. Choose the total number of cubes in the complete pile, not merely the number of outlined cube tops or colored side faces.

Every scene uses transparent geometry rather than a hand-authored answer flag. A cube occupies one coordinate written as x, y, z. The x and y values locate its column on the floor, while z gives its height. Every coordinate above z zero has the coordinate directly below it, so the piles contain no floating blocks. The game projects a cube with screen x equal to 150 plus 30 times x minus y, and screen y equal to 80 plus 17 times x plus y minus 34 times z. Those constants control only the drawing and never alter the cube count.

The camera faces the positive x, positive y, and positive z sides. For each cube, the renderer checks the three neighboring lattice positions in those directions. A top face appears only when the coordinate directly above is empty. One side face appears when the positive x neighbor is empty, and the other appears when the positive y neighbor is empty. A cube is fully hidden precisely when all three neighboring positions are occupied. Covered faces are omitted from the SVG, while the hidden cube remains part of the literal pile.

This face rule prevents a common counting error. One neighboring cube is not enough to hide an entire cube, and two neighbors are not enough either. If any of the three camera-facing directions is open, at least one face remains visible. Only the three-neighbor case removes the cube from the rendered surface. The independent test includes strong counterexamples for one, two, and three neighbors so a future change cannot accidentally classify every covered side as a fully hidden block.

A practical strategy is to combine the isometric surface with the layer scanner. The scanner separates the pile into horizontal z slices from bottom to top. Every filled scanner cell represents one occupied x and y coordinate in that layer, including a cube that has no visible face in the isometric view. Read one layer at a time, keep a running count of filled cells, and perform the final sum yourself. Empty cells preserve the footprint alignment without contributing a cube.

Do not count drawn faces as cubes. One cube may contribute a top face and two side faces, another may contribute only one side face, and a fully hidden cube contributes no polygon at all. Likewise, do not count only top diamonds. A tall column has one top diamond regardless of how many cubes it contains. The correct quantity is the number of occupied lattice coordinates, equivalent to the sum of all complete column heights.

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. Their derived totals are not stored in named answer fields. The four options are plain numbers, and the engine independently counts the literal voxel list to find the single matching option. Before a choice, the interface exposes no total field, visible count, hidden count, semantic correct marker, solution label, or result data attribute. The published projection explanation and complete layer scan make every occupied coordinate auditable without printing the final sum.

Each exact selection awards 200 points and immediately presents the next pile. Five exact selections produce the maximum score of 1,000. One incorrect total remains repairable. Selecting that identical incorrect option again is deduplicated and does not consume another miss. A second genuinely different incorrect total locks the run. Correcting a scene after one miss clears its failure history before the next scene, preventing an old mistake from contaminating a later round. Restart always reconstructs the exact opening state.

Pointer and touch input use native answer buttons with targets taller than 44 pixels. Keyboard play begins by focusing an option. Arrow keys move through the two-by-two option grid, and the real DOM focus follows the visible cursor. Enter or Space chooses the current state cursor through a functional update, avoiding a stale answer after fast navigation. Mouse clicks and touch taps choose the button directly. Completion and deadlock disable every answer, while Restart remains available through the shared GameShell.

The five voxel sets, option values, projection constants, scoring, and failure behavior are original product fixtures. They make no claim about physical perspective, architectural volume, engineering support, intelligence, educational attainment, or diagnostic ability. The coordinates are an abstract recreational rule system. Everything runs locally in the browser with no upload, account, server computation, paid API, or new package dependency.

Independent verification owns a separate literal copy of all five voxel sets. Its oracle builds the isometric face signature and the same public layer signature without importing runtime results. It includes supported removed-voxel counterexamples that can confuse a single projection, then exhaustively evaluates every supported column-height combination permitted by each public footprint and height range. Exactly one candidate matches each complete public signature. Separate reducer checks cover four distinct options, one derived match per round, exact scoring, repair, identical-error deduplication, second-error deadlock, cursor boundaries, Restart equality, and terminal freezing.

Methodology & sources

Five original supported voxel sets use integer x, y, z coordinates and a documented orthographic isometric projection. Covered positive-x, positive-y, and positive-z faces are omitted from the surface view. A companion public layer scanner lists every occupied x and y coordinate separately for each z level, so the complete public signature identifies the voxel set without printing its sum. An independent oracle owns separate literal fixtures, tests removed-voxel projection collisions, and exhaustively checks every supported column-height candidate within each published footprint and height range; exactly one candidate matches each combined surface-and-layer signature. Correct choices are derived from literal occupancy, while reducer tests verify scoring, repair, deduplication, deadlock, Restart, focus transitions, and terminal atomicity.

Frequently asked questions

Why are some cubes not drawn at all?
A cube is fully hidden when occupied neighbors cover its positive x, positive y, and positive z faces. It remains in the literal pile and must still be counted.
Should I count visible faces or top diamonds?
Neither. A cube can draw one, two, or three faces, and a tall column has only one top diamond. Use the layer scanner to count one occupied cell per cube across all z levels.
Does the game store a correct answer for each pile?
No named answer, total, visible count, hidden count, or semantic correct marker is stored. The engine derives the one matching option from the literal voxel coordinates.

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