A 5 by 15 by 27 cuboid is made up from 2025 unmarked wooden unit cubes.
Each face of the cuboid is assigned a different integer from 0 to 5 and that number is written on every unit square making up that face.
The 2025 cubes are separated.
The value of a unit cube is the sum of the numbers (if any) on its faces.
Given that the sum of all the numbers on all the faces is 2025, how many cubes have an odd value?
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