Mathematics · the experiment
Fill the line without a gap
A line of 48 integers and copies of F₄ = {0, 7, 9, 16}. Place them without overlap and see how far you can fill the line without leaving a gap.
1 · No tiling2 · The long run3 · The cubes
1 · Fit the first copies together
Beginner
According to the paper, what can shifted copies of Fₙ never do?
One copy is already placed. Pick a position, place the copy, repeat: fill a gap-free run of 8 consecutive integers.
2 · Outgrow F₄
Intermediate
For n = 4, what length of gap-free run does the paper give?
Keep going on the same line, or start over: fill a gap-free run of 22 consecutive integers. Stuck? Remove some copies.
3 · Move to cubes
Expert
To guarantee h = 5 coronas, the author takes n = 3h + 4. How many cubes does the shape then have?
Line filled
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