Questions tagged [tiling]

A geometric packing puzzle in which a number of shapes have to be assembled into a larger shape, generally without overlaps or gaps.

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How many of the 16 cells of the grid could contain the black dot?

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
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When Beatrix stops placing dominoes on a 5x5 board, what is the largest possible number of squares that may still be uncovered?

Beatrix places dominoes on a 5x5 board, either horizontally or vertically, so that each domino covers two small squares. She stops when she cannot place another domino, as in the example shown in the ...
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7x10 floor and a 8x8 and a 6x1 carpet, only one cut allowed

We have a 8x8 carpet, we can do only one cut of any complexity and also we have an uncuttable 6x1 carpet. We need to fill a 7x10 space using those 2. The 8x8 can only be cut into two pieces. We have ...
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Can you use triangular tiles to form a rectangle of size 2016 cm by 2021 cm?

Beginner puzzle This puzzle is intended to be suitable for people who are new to puzzle solving. Clarification: Both experienced solvers and new solvers are welcome to post solutions to this puzzle. ...
• 13.8k
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Is it possible to arrange the free n-minoes of orders 2, 3, 4 and 5 into a rectangle?

To be explicit, the shapes pictured below, with reflections permitted. Can these be packed into a rectangle? This puzzle arose from discussion on r/mathmemes. No solution was posted (and I don't know ...
• 3,168
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Filling a rectangular grid with holes using tetrominoes

There is a rectangular grid of $R$ rows and $C$ columns. $R \times C \bmod 4$ of the cells are painted black, and all other cells are white. In other words, there are at least 0 and at most 3 black ...
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Tile dominoes in a 3x10 space [closed]

How many ways are there to tile 1x2 (unmarked) dominoes in a 3x10 space? This is a harder version of Tile dominoes in a 2x10 space, since that was too easy.
• 989
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Packing 25 three-dimensional N pentominoes into a 5x5x5 cube

The puzzle contains 25 identical pieces that look like this: To be explicit, the piece is composed of five cubes. In the picture, three cubes form the base, and two cubes form the overhang. The goal ...
• 3,168
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Tiling a 16x16 square with 1x4 rectangles

Consider a 16x16 square subdivided by grid lines into unit squares. It is easy to completely tile (no overlaps, no gaps) this square with 64 1x4 rectangles. Each 1x4 rectangle in the tiling (no ...
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Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?

Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9? No two rectangles can be the same size.
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Flipped Einsteins in the Einstein Tiling

The single-tile aperiodic tiling by Goodman-Strauss, Kaplan, Myers and Smith has been all the rage recently: In this tiling a minority of tiles, coloured purple above, are flipped with respect to the ...
• 7,820
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Boxeslayers to the rescue

This is about layering boxes, not about slaying them. We have 1,830 2×5 boxes to stack safely as 10 alternating contiguous layer patterns of 183 boxes each. Layers have identical silhouettes that fit ...
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How to fully tile an 8 by 8 square with Z-tetrominoes?

Is it possible to fully tile an 8 by 8 square grid using only Z-tetrominoes? (I don't know the answer...)
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Popping pentominoes

I started with the following configuration: I then popped a few spots in the shape of the same pentomino to arrive at this configuration: The shapes did not overlap and I was allowed to rotate and ...
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Set of magic polyominoes that can tile a square

Let's first look at this square grid of numbers. The 9 squares in yellow is what we are looking at and the green numbers are the sums for the digits within the rows and columns. The red squares are ...
• 621
1 vote
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Arranging shapes into a similar shape

The goals if possible. Goal 1. In the image there are 12 shapes each containing 15 cells. Take any 3 shapes from the set and arrange them into any new shape, 2 example shapes that you could use are ...
• 621
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Polyominos packing into a square

Rules of the game: Take a square grid nxn. Populate the grid with polyonimoes of area size 1 to area of 9. Polyominoes can be any shape. There must be one each of every size polyomino in every row ...
• 621
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Smallest square that can pack thin digits

If we draw the digits 0 to 9, segmented into squares, across a rectangle of 2x5 (except the 1) they use up 81 total squares. Is it possible to pack them all into a 9x9 grid. What is the smallest n by ...
• 621
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Tiling a chessboard

Say I have an eleven by eleven chessboard, so there's 121 squares total. I remove the centermost piece so there's 120 pieces. I want to tile the chessboard with 1x4 or 4x1 pieces in a way that none of ...
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Seven octahedral nets to cover an octahedron

After solving Cover a single cube with FIVE identical cube nets I had the idea for this puzzle, which may be regarded as a natural generalisation to triangular grids. Find two different nets, A and B, ...
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Cover a single cube with FIVE identical cube nets

Start with five identical cubes: Your challenge: Cut and unwrap all five cubes into five identical cube nets. Show how to re-fold these five cube nets to form the surface of a single larger cube, ...
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Covering a room with 34 carpets

There are 34 rectangular integers less than 100 which are the product of two primes. Can a room be covered precisely (no overlaps, etc.) with the 34 rectangles that have as areas these products?