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JBMO-SL 2005 C2

Government of Greece wants to change the building. So they will move in building with square shape 2005×20052005 \times 2005. Only demand is that every room has exactly 2 doors and doors cannot lead outside the building. Is this possible? What about a building 2004×20052004 \times 2005 ?

Dataset text NuminaMath olympiads. Quoted with source.

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