Comments by sph0lt0n

sph0lt0n Some lootboxes are unsolvable 2026-02-15 17:52 UTC

Some of the puzzles create by lootboxes are unsolvable -- they correspond to configurations with odd parity. The parity check

    -- Check if can be solved
    local inversions = 0
    for i = 1, #raw_pos do
        for j = i + 1, #raw_pos do
            if raw_pos[i] > raw_pos[j] then
                inversions = inversions + 1
            end
        end
    end

incorrectly includes the parity of the blank (9), which allows some configuration with odd parity to pass this test.

I'd recommend the following code change:

    -- Check if can be solved
    local inversions = 0
    for i = 1, #raw_pos do
        for j = i + 1, #raw_pos do
            -- Only count inversions for tiles 1-8. 
            -- Skip the blank tile (9) to ensure stable parity.
            if raw_pos[i] ~= 9 and raw_pos[j] ~= 9 then
                if raw_pos[i] > raw_pos[j] then
                    inversions = inversions + 1 
                end
            end
        end
    end

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