There is trouble in the BOSS facilities department. A small secure electronics room is being refurbished, and the contractors are fitting a new anti-static floor around three pieces of essential equipment that are far too large, heavy to move. In any case they have been bolted down for security and the engineers are worried about stripping the threads if they try to remove the bolts.
The floor is divided into a 6 × 6 grid as shown on the floor plan below. The three grid squares occupied by the equipment are labelled B2, F3 and D5 using something like chess notation.
The new floor covering has been provided by the manufacturer as a pack of rigid rectangular panels, each exactly one grid square wide and three squares long, and the panels can be laid either horizontally or vertically on the floor plan.
The supplier worked out that:
- the room is 36 square meters in area
- the three equipment plinths occupy 3 square meters
- so they need to cover 33 square meters.
Since each panel is 3 square meters in area they have provided exactly 11 panels. Can you find a way to lay them to cover the floor? In order to preserve their anti-static properties and rigidity you are not allowed to cut or bend them.
Secure data store B71 Floor Plan (STRAP)
The black squares mark the 3 permanent equipment plinths.
The panels may be placed horizontally or vertically, but they may not overlap, be cut, stick outside the room or cover one of the equipment plinths.
If you think it can be done, show how.
If you think it can’t be done explain why not.
Hint 1
The fact that the areas match tells you that a tiling might exist. It does not prove that one does.
Try colouring the squares of the floor in a repeating pattern.
Hint 2
Use three colours, repeated diagonally across the board.
Can you colour the floor so that every horizontal or vertical 1 × 3 panel must cover exactly one square of each colour?
Bonus challenge: can you establish your answer without trying any panel arrangements at all?