Programs and verification

Color masks → column spans → largest drop

For each curve color, the program selects nearby RGB values. In every occupied column it measures the distance between the first and last selected pixel, then takes the largest span.

Simplified pseudocode · helpers summarize pixel processing

for color in curve_colors:
    mask = pixels_close_to(color)
    score[color] = largest_column_span(mask)
return largest_score_color(score)

Evidence checks. Rejects missing curves and a winning margin smaller than two pixels.

Dark pixels → least-squares circle → nearest dot

The program selects dark contour pixels and fits x² + y² = 2cx·x + 2cy·y + c by least squares. It estimates each colored dot’s center by averaging its pixel coordinates.

Simplified pseudocode · helpers summarize pixel processing

arcs = select_dark_pixels(image)
center = fit_circle_least_squares(arcs)
dots = measure_colored_dot_centers(image)
return nearest_dot(dots, center)

Evidence checks. Checks fit error, coverage around the circle, marker sizes, and separation between the nearest two dots.

White pixels → connected rooms → shared neighbor

A flood fill groups white pixels connected through horizontal or vertical neighbors. Regions touching the image boundary are exterior space. The program samples beside the long edges of both gates and compares their enclosed-room labels. It labels regions at a conservative four-pixel scale.

Simplified pseudocode · helpers summarize pixel processing

rooms = label_connected_white_regions(image)
rooms = remove_exterior_regions(rooms)
a = rooms_beside(green_gate)
b = rooms_beside(purple_gate)
return bool(a & b)

Evidence checks. Checks image dimensions and gate geometry; rejects gates with no resolved enclosed neighbor.

Cell brightness → rotation and subtraction → template match

The cyan frame locates an 11 × 11 grid. Brightness inside each cell determines whether it is dark. The program removes cells that are also dark in a half-turned copy, then compares the remaining set with four stored glyph patterns across possible placements.

Simplified pseudocode · helpers summarize pixel processing

dark = read_dark_grid_cells(image)
rotated = {(10-r, 10-c) for r, c in dark}
remaining = dark - rotated
return closest_glyph_template(remaining)

Evidence checks. Rejects ambiguous cells, implausible counts, excessive template mismatch, and close matches.

Colored objects → ordered commands → bounded counter

Connected colored pixels form objects. Proportions and filled area distinguish gauge blocks from triangles. A triangle’s center of mass relative to its bounding box determines its direction. The program orders commands from left to right and updates the level.

Simplified pseudocode · helpers summarize pixel processing

level = count_gauge_blocks(image)
for op in read_arrows_left_to_right(image):
    if op == "up":
        level = min(4, level + 1)
    else:
        level = max(0, level - 1)
return level

Evidence checks. Requires eight recognizable commands with enough horizontal separation and at most four starting blocks.