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Questions tagged [packing]

A puzzle that involves arranging objects optimally in order to fit in a specified space.

11
votes
2answers
476 views

Ziggy - Make a square from 8 polyomino pieces

A few years ago I created a small packing puzzle that I'd like to share here today. The puzzle is based on the fact that $1+2+3+4+5+6+7+8 = 6^2$. It consists of 8 zig-zag polyomino pieces, ranging in ...
5
votes
1answer
2k views

Is there only one solution to the “Ten Penny Puzzle” or more?

Not knowing the dimensions of the square in the Ten Penny Puzzle I ask if there is more than one unique solution that isn't a reflection/mirror of the one shown in the video, if you know the ...
13
votes
1answer
357 views

The crossword packing puzzle

To describe it shortly, it's like Scrabble Tetris. Except the quality is much lower. Fit all the pieces inside the grid The pieces can NOT be rotated No piece can be placed on top of the crossed ...
3
votes
2answers
463 views

The farmer and the olive trees

A farmer has a rectangular ground of 100 m by 50 m, he wants to plant olive trees, in sufficiently spaced ways (to avoid exhaustion by the roots) at least 10 meters from each other. How much can one ...
12
votes
2answers
767 views

Near-fill with 3x1 long triominos, how to do a different void square than the center square?

It's rather easy to fill a $7 \times 7$ board with 16 long triominos, leaving the center square void: see the picture below. But if I want to move the void square in another position, where else could ...
0
votes
1answer
1k views

Packing circles in a rectangle [closed]

You have a rectangle of dimensions $l \times b$ where $l\geq b \geq 1$ and $l,b \in \mathbb R$. How many circles of diameter one unit can be fitted inside this rectangle without overlapping? (Touching ...
4
votes
1answer
236 views

What's the best way to pack the disks?

Here's a puzzle given me by some folks at Science Olympiad. I haven't been able to solve it yet. You have 50 disks, each 1 cm in diameter. On the table are four concentric rings: the first with a ...
1
vote
0answers
198 views

How many cylinders in a cube [closed]

Could someone please help me with this math question: How many cylinders with a diameter of $7.44 cm$ and a height of $4.9 cm$ can fit in a cube of $1m \times 1m \times 1m$?
-6
votes
2answers
177 views

Pack a box with beach stuff [closed]

You have to place the objects so that no object touches any other or any purple. This obviously needs a computer program: Packer It can be done - it may be possible to do it more than one way.
8
votes
1answer
201 views

A Railcar for L. & J. Railroad

In the land of the tetrominos, the twins L. and J. have set out to revolutionize travel by rail. Contemporaries' passenger cars are boxy and boring, and humdrum symmetric passenger ...
12
votes
3answers
617 views

Rearranging connected tiles

Sorry. The previously posted image contained a mistake. Tile D2 was shown with a 180 degree rotation. The image has now been corrected. This is a straight-forward arrangement puzzle. You are ...
18
votes
4answers
1k views

The 2 million, er, 20 dollar problem

Alfred is a guy who really likes solid shapes. He also really likes to keep his money in his wallet. What makes him the happiest? Getting a boxful of shapes at the Cheap Solids Store! The store has ...
2
votes
1answer
505 views

What's the smallest chemical elements word search that can be made?

I want the elements from 1 to 118, their names, atomic numbers and symbols including capitalization. There is one important rule that makes things a little more difficult: No item can be ...
36
votes
7answers
4k views

A Surprising Circle Packing

A grocery store has a long, skinny box, with no top, that it uses to display soda. The box is two soda cans wide and 200 soda cans long. You can neatly fit 400 cans in this box, using two rows of 200, ...
5
votes
1answer
239 views

Optimal size of n circles to fit an area

Let us say that I have a rectangular area that has to always look "filled" with circles. (the void spaces with the given number of circles should be minimal)(Goal) Let us assume that, I am also told ...