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RobPratt
RobPratt
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Edited the last paragraph to clarify its meaning
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Pranay
Pranay
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While traveling in Europe recently, I bought a tiling puzzle for my daughter. (It is a Grimm’s wooden puzzle, exactly like the one in this link.) The puzzle contains 18 congruent tiles, each of which is a 30°-120°-30° isosceles triangle. They can all be arranged inside a wooden hexagonal frame with no gaps and no overlaps as follows:

perfect tiling

However, my daughter now insists on starting with the following configuration because the pieces fit nicely along the corners of the hexagonal frame:

initial configuration

But she’s unable to fit all the remaining tiles inside the frame. Can you help her maximise the number of tiles that can be fit inside the rest of the frame with no overlaps?

While traveling in Europe recently, I bought a tiling puzzle for my daughter. (It is a Grimm’s wooden puzzle, exactly like the one in this link.) The puzzle contains 18 congruent tiles, each of which is a 30°-120°-30° isosceles triangle. They can all be arranged inside a wooden hexagonal frame with no gaps and no overlaps as follows:

perfect tiling

However, my daughter now insists on starting with the following configuration because the pieces fit nicely along the corners of the hexagonal frame:

initial configuration

But she’s unable to fit the remaining tiles inside the frame. Can you help her maximise the number of tiles that can be fit inside the rest of the frame with no overlaps?

While traveling in Europe recently, I bought a tiling puzzle for my daughter. (It is a Grimm’s wooden puzzle, exactly like the one in this link.) The puzzle contains 18 congruent tiles, each of which is a 30°-120°-30° isosceles triangle. They can all be arranged inside a wooden hexagonal frame with no gaps and no overlaps as follows:

perfect tiling

However, my daughter now insists on starting with the following configuration because the pieces fit nicely along the corners of the hexagonal frame:

initial configuration

But she’s unable to fit all the remaining tiles inside the frame. Can you help her maximise the number of tiles that can be fit inside the rest of the frame with no overlaps?

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Pranay
Pranay
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Maximize the number of triangular tiles that can fit inside a hexagon after three tiles are placed

While traveling in Europe recently, I bought a tiling puzzle for my daughter. (It is a Grimm’s wooden puzzle, exactly like the one in this link.) The puzzle contains 18 congruent tiles, each of which is a 30°-120°-30° isosceles triangle. They can all be arranged inside a wooden hexagonal frame with no gaps and no overlaps as follows:

perfect tiling

However, my daughter now insists on starting with the following configuration because the pieces fit nicely along the corners of the hexagonal frame:

initial configuration

But she’s unable to fit the remaining tiles inside the frame. Can you help her maximise the number of tiles that can be fit inside the rest of the frame with no overlaps?