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11 votes

Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?

Yes you can and this is how you do it:
PDT's user avatar
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-4 votes

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

Yes this is possible. The board is 25x25... A ring of 2x2 tiles round the exterior would leave an internal space of 21x21. This internal space would allow exactly 7x7 of the 3x3 tiles (3x7)x(3x7).
VariableSquid's user avatar
37 votes

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

Very similar to @Bubbler's solution but perhaps a bit simpler:
Albert.Lang's user avatar
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39 votes
Accepted

Can you tile a 25 x 25 square with a mixture of 2 x 2 squares and 3 x 3 squares?

I think the answer is Consider the following image: Generalizing this result, the question "For which $n$ can an $n \times n$ square be tiled with $2 \times 2$ and $3 \times 3$ squares?" ...
Bubbler's user avatar
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1 vote

Make a square table top with the minimal needed amount of straight cuts

For completeness: A suboptimal answer I had in mind was:
Retudin's user avatar
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15 votes
Accepted

Make a square table top with the minimal needed amount of straight cuts

It can be done in (but not without 30 characters)
loopy walt's user avatar
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10 votes

Make a square table top with the minimal needed amount of straight cuts

Another answer matching the current best number of cuts, but using only horizontal and vertical cuts (my brain doesn't work well with triangles).
calvenable's user avatar
3 votes
Accepted

Build a slanted pyramid with ten L-shaped blocks

user1502040's user avatar
13 votes

Make a square table top with the minimal needed amount of straight cuts

Here is an answer with only straight cuts. See image below:
Lezzup's user avatar
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3 votes

Make a square table top with six (or fewer) pieces

My (boring) 6 solution; and (cool) 7 piece solution for inspiration.
Retudin's user avatar
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6 votes
Accepted

Make a square table top with six (or fewer) pieces

For a start, here is a 6-piece solution. From there you can find some variations. Here is a less boring one.
Florian F's user avatar
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3 votes

Circles crossing every cell of an NxN grid

Here are two solutions that yielded the best-known values (not necessarily optimal). $N=12$: $N=13$:
RobPratt's user avatar
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5 votes

Circles crossing every cell of an NxN grid

UPDATE: I found some nice symmetric solutions: N = 12 N = 14 N = 18 I found some new solutions N = 12 N = 13 N = 14, love that circle that breaks symmetry N = 15 N = 16 N = 17 N = 18 N = 19, ...
Dmitry Kamenetsky's user avatar
4 votes

Circles crossing every cell of an NxN grid

Making a community wiki so that all the answers are kept in one place. Anyone can edit it. N Circles (Current Best Known Upper Bound) Credit 1 1 trivial 2 1 trivial 3 2 user1502040 4 2 ...
6 votes

Circles crossing every cell of an NxN grid

I think I am still a fan of concentric circles. Modulo some adjustments for the corners. Here is a 20-grid covered with 14 circles.
Florian F's user avatar
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1 vote
Accepted

April Fools Origami Update

Retudin's user avatar
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0 votes

Circles crossing every cell of an 8x8 grid

I think the correct answer is 4 but I don't know how to draw the solution. Anyway, you can imagine the 8x8 grid as four 4x4 grid and, for each of these, draw a circle that cross all 4x4 squares, like ...
YourDarkIntentions's user avatar
5 votes

Circles crossing every cell of an NxN grid

My best effort: 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 11, 11, 13, 16, 17, 19, 20, 20, 22. The larger ones are definitely suboptimal.
user1502040's user avatar
4 votes
Accepted

Recursive rhombic dodecahedron tiling

Not sure this is the correct answer, but will post it. This Wikipedia page about Rhombic dodecahedral honeycomb states So if the formula is the same as ...
Weather Vane's user avatar
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8 votes
Accepted

Is it possible to fill an arbitrarily large hex grid completely given these rules? #2

I claim the answer is because
Deusovi's user avatar
  • 146k
8 votes

Is it possible to fill an arbitrarily large hex grid completely given these rules?

I claim that the answer is and here's why:
Deusovi's user avatar
  • 146k
10 votes

Circles crossing every cell of an 8x8 grid

Bonus version: (I claim without proof that this is optimal)
Sunny Lu's user avatar
  • 3,140
14 votes
Accepted

Circles crossing every cell of an 8x8 grid

Here is my first try. I wonder whether one can do better. (actually it is not true. My first shot was 16 small circles...)
Florian F's user avatar
  • 29.9k
12 votes
Accepted

origami WAVE t2

Here we go... Sorry, it is not the "orthogonal" type. Here is a cleaner image. Fold on the red lines. It might not be obvious at first, but everything falls in place.
Florian F's user avatar
  • 29.9k
0 votes
Accepted

Logic and Geometry Problem #6

Can there be a square on which neither Red nor Blue can place a stone?
GoblinGuide's user avatar
9 votes
Accepted

ORTHOGONAL origami FISH t8

Here it is. Fold vertically then horizontally.
Florian F's user avatar
  • 29.9k
4 votes
Accepted

origami USHAPE t3

Folding along the red lines:
A username's user avatar
12 votes
Accepted

origami FISH thickness 8

Magma's user avatar
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