Ant Cubes
A cuboid is filled up with 4608 little cubes of dimensions An ant passes through a straight line, connecting two opposite vertices of the cuboid.
How many little cubes does the ant pass through?
Note: Cubes are only counted if the traversal passes through them, so if the traversal only touches a vertex or an edge separating cubes within the cuboid, then it is not considered to pass through the adjacent cubes.
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1 solution
Number of cubes ant pass = Length + Width + Height – HCF(Length, Width) – HCF(Width, Height) – HCF(Length, Height) + HCF(Length, Width, Height)
Therefore, required Number of cubes equal to 12 + 16 + 24 - HCF(12,16) - HCF(16,24) - HCF(12,24) + HCF(12,16,24) = 12 + 16 + 24 – 4 – 8 – 12 + 4 =32