Skip to main content

Questions tagged [packing]

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

Filter by
Sorted by
Tagged with
12 votes
2 answers
990 views

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 ...
ApexPolenta's user avatar
  • 2,904
3 votes
1 answer
331 views

Build a slanted pyramid with ten L-shaped blocks

Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Use 10 of the above L-shaped pieces to make the following shape:
Will.Octagon.Gibson's user avatar
7 votes
1 answer
338 views

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube?

Can 42 1x2x4 cuboids be packed into a 7x7x7 cube without cutting any of them? Assume that all cuboids have their axes parallel to the axes of the big cube. I tried using https://www.jaapsch.net/...
mathlander's user avatar
  • 1,261
14 votes
1 answer
387 views

Yet another pentomino puzzle

Just rearrange the 13 checkered polyominoes shown below to form a chessboard. The solution is unique and unusual. Clarification: The pieces may be reflected; the coloring on the back is as if the ink ...
username4231's user avatar
6 votes
2 answers
436 views

Pawns and a chessboard with no three aligned

This little problem crossed my mind and appeared to be not quite trivial. How can you place P pawns on a chessboard with the constraint that no pawn is exactly midway between two other pawns? Sure ...
Florian F's user avatar
  • 30.6k
13 votes
3 answers
557 views

Packing a 3x3x3 cube with three congruent polycubes

A polycube is a solid three-dimensional connected figure formed by joining one or more unit cubes face to face. Polycubes can be thought of as the three-dimensional generalization of polyominoes. Can ...
Will.Octagon.Gibson's user avatar
18 votes
3 answers
951 views

PSE Advent Calendar 2023 (Day 8): A Quilt for Santa

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2023. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > Mrs. Claus ...
Aaron Windsor's user avatar
3 votes
1 answer
201 views

Packing a 3xMxN-box with copies of a single tetracube

There seems to be no solution for packing a 3xMxN-box with copies of this tetracube. Does anybody know of a proof that this is impossible or is this still an open question?
Werner Nickel's user avatar
27 votes
2 answers
2k views

12 piece cube packing puzzle

Consider the following hexacube (made from 6 unit cubes): GOAL: Pack a 3 x 3 x 3 cube using three of these hexacubes plus nine unit cubes. This puzzle comes from: https://puzzlewillbeplayed.com/333/...
Will.Octagon.Gibson's user avatar
11 votes
3 answers
1k views

Can you pack these pentacubes to form a rectangular block with at least one odd side length other the side whose length must be a multiple of 5

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. Consider the following pentacube (made from 5 unit cubes): It is possible to pack four of these pentacubes to form a 2x2x5 ...
Will.Octagon.Gibson's user avatar
5 votes
1 answer
2k views

How many ways are there to solve the Mensa cube puzzle?

The Mensa cube is a puzzle in which a solid cube has been partitioned into $N=11$ rigid parts. The goal of the puzzle is to re-assemble the cube from its parts and place it back in its rigid box. See ...
fromscratch's user avatar
18 votes
2 answers
1k views

Can you pack these tetracubes to form a rectangular block with at least one odd side length?

Consider the following tetracube (made from 4 unit cubes): It is easy to pack two of these tetracubes to form a 2x2x2 rectangular block. And from that simple packing it is easy to pack any ...
Will.Octagon.Gibson's user avatar
8 votes
3 answers
618 views

Cutting a square into integer triangles

You are given a square piece of paper with size 10x10 units. What is the most number of triangles that can be cut from this square, such that: Each triangle has integer sides. Each triangle is ...
Dmitry Kamenetsky's user avatar
8 votes
4 answers
891 views

Smallest rectangle to put the 24 ABCD words combination

Put in the smallest possible size board all combination of 4 quantity of letters. Crossword must be connected. And can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters Example for:...
Rodolfo Kurchan's user avatar
6 votes
2 answers
354 views

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 ...
humn's user avatar
  • 21.9k
6 votes
0 answers
226 views

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 ...
Maff's user avatar
  • 621
1 vote
0 answers
156 views

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 ...
Maff's user avatar
  • 621
8 votes
2 answers
374 views

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 ...
Maff's user avatar
  • 621
7 votes
2 answers
403 views

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 ...
Maff's user avatar
  • 621
-4 votes
2 answers
143 views

Smallest rectangle that fits the first 10 rectangles [closed]

What is the area of the smallest rectangle that can fit 10 rectangles with areas 1 to 10, inclusive? Rectangles must have integer sides and cannot overlap.
Dmitry Kamenetsky's user avatar
13 votes
1 answer
347 views

Ernie and the disappointing drill bits

I was driving to Ernie's place a couple of days ago, with Ernie in the passenger seat, when we drove past an old building with a faded sign reading Lar's Tool's. Beneath it, scrawled on the front wall ...
Penguino's user avatar
  • 14k
4 votes
1 answer
182 views

Packing the Primes

Here is a 5x4 rectangular wordsearch (area 20) containing the primes between 1 and 100, {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97} (numbers in any ...
Amoz's user avatar
  • 27.7k
13 votes
4 answers
904 views

What approach can I use to solve this wooden packing puzzle?

I am looking for an approach to solve a wooden packing puzzle which my three-year-old got as a present. We enthusiastically unpacked and disassembled the puzzle when she got it. (It came put-together ...
justfortherec's user avatar
7 votes
1 answer
697 views

Solving a 5x5 pentomino with only certain shapes

I have a physical Pentomino puzzle lying around, which contains 2 F pieces, one Y piece, one T piece and one W piece. The area into which the squares are supposed to fit in is just a little under 6 ...
Cheese Macken's user avatar
8 votes
1 answer
512 views

Pentomino - is there any solution with the straight-bar piece in the middle of a rectangle?

Is there a solution for a straight-bar piece not touching the edge of the rectangle? By rectangle solution, I mean either one of the patterns 15x4, 12x5, or 10x6. By straight-bar piece, I mean the ...
Przemyslaw Remin's user avatar
40 votes
6 answers
2k views

Packing pentominoes in a circle

You want to prepare a pizza of 12 flavors. You have 12 oddly-shaped pieces of cheese that you decide to use for the pizza. The shapes happen to be ... Oh, well, forget it! This isn't going to be ...
Florian F's user avatar
  • 30.6k
-2 votes
1 answer
161 views

15 x 15 polyomino

You cannot move the red squares You cannot rotate the blocks You cannot have 2 block of the same color touching each other, not even diagonally (by their corners) Grey blocks cannot touch a red square,...
Alain Reve's user avatar
3 votes
1 answer
223 views

Block fill in date puzzle

I have been trying this puzzle for HOURS!!! The goal is the fit all the pieces but not cover Aug or 1. You can rotate the pieces. Credit to www.dragonfjord.com The link shown at the bottom of the ...
Slayveer's user avatar
12 votes
1 answer
292 views

Please help me fix my intestine

Due to some unfortunate events involving a teleporter and a ceiling fan I had my innards spread all over the place. Interestingly my intestine was split into equal sized chunks representing all the ...
Florian F's user avatar
  • 30.6k
4 votes
2 answers
415 views

Polyominoes inside a 10x10 grid

Can you place five dominoes, five trominoes, five tetrominoes, five pentominoes and five hexominoes inside a 10x10 grid, such that: No two polyominoes overlap No two polyominoes of the same size (by ...
Dmitry Kamenetsky's user avatar
4 votes
3 answers
550 views

Multi-colored polyominoes inside a 7x7 grid

Can you place four red trominoes, four green tetrominoes and four blue pentominoes inside an 7x7 grid, such that: No two polyominoes overlap No two polyominoes of the same color touch each other ...
Dmitry Kamenetsky's user avatar
8 votes
1 answer
222 views

Tetromino in a Pentomino Lair

Inspired by this question: Can you fit twelve pentominoes (not necessarily distinct) and one tetromino inside a 10 x 10 grid such that they do not overlap or touch each other orthogonally (...
hexomino's user avatar
  • 137k
11 votes
3 answers
1k views

Fitting pentominoes inside a 10x10 grid

What is the most number of pentominoes that you can fit inside a 10x10 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically)? Bonus: what is the most number ...
Dmitry Kamenetsky's user avatar
10 votes
3 answers
1k views

Ten tetrominoes inside an 8x8 grid

Can you place ten tetrominoes inside an 8x8 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically) ?
Dmitry Kamenetsky's user avatar
3 votes
1 answer
357 views

How many distinct pentominos can be placed on a 8×9 board?

Upon proving optimality of an 8-pentomino solution for an 8×8 board, I was curious to see whether there is a 9-pentomino solution for an 8×9 board, namely a way to arrange 9 distinct pentominos within ...
user21820's user avatar
  • 1,236
14 votes
3 answers
2k views

How many distinct pentominoes are possible to place on an 8 x 8 board?

Rules Place some pentominoes into an 8 x 8 grid. They do not touch each other. They can touch only diagonally (with corner). Pentominoes cannot repeat in the grid. Rotations and reflections of a ...
Ignac's user avatar
  • 141
13 votes
2 answers
516 views

Put three pieces of cake into a round box

You're about to cut three pieces from a large cake to put in a round box of radius 1. If the pieces must be congruent triangles, and cannot overlap, what shape gives you the maximum amount of cake?
Eric's user avatar
  • 6,536
22 votes
3 answers
2k views

Dividing a piece of land

Alice and Bob try to divide a piece of land $D$, shaped in a perfect closed disk of radius 1. Alice moves first to mark some finite (at least one) number of points in $D$. Bob then draws any number of ...
Eric's user avatar
  • 6,536
7 votes
1 answer
1k views

Can you stop the falling piano with 23 nets?

MIT's Baker House has a tradition of dropping an irrepairable piano six floors every Drop Day, the last day one can drop a class without penalty (the 2022 date is 19 April). This year, in order to ...
Parcly Taxel's user avatar
  • 7,720
8 votes
2 answers
450 views

How many squares can a limp queen move to?

Consider a large chessboard. A limp rook is a chess piece that moves one step orthogonally, but it turns $90$ degrees after every move. The limp rook makes some moves, not crossing over its own path, ...
littlecat's user avatar
  • 343
6 votes
2 answers
589 views

Jigsaw puzzle: packing pentominoes into a rectangle

I've got this jigsaw puzzle that I can't figure out. The major problem is that there are no signposts on whether a piece is in the right place. How does one get all the pieces into the 6x10 container? ...
Allure's user avatar
  • 163
9 votes
2 answers
3k views

Social distancing in a 5x5 room [duplicate]

I have booked a square meeting room that is 5 by 5 meters. Our Covid-19 policy says that each person must be at least 1.5 meters away from any other person. What is the highest number of people that ...
Dmitry Kamenetsky's user avatar
4 votes
2 answers
336 views

Arrange the wooden blocks in the box

Little Johnny is the naughtiest child in the kindergarden today. The kind who always wants more than the other children. When he saw that little Tim was playing with the same set of wooden blocks as ...
Florian F's user avatar
  • 30.6k
6 votes
2 answers
2k views

Eighteen is not seventeen

This question is not the same as Adding coins inside a ring of coins From a pile of equal size perfectly round coins take eighteen and make a perfect ring. Show that you can fit at least sixteen more ...
loopy walt's user avatar
  • 21.3k
10 votes
2 answers
632 views

Adding coins inside a ring of coins

17 identical coins with diameter 1 are lying flat on a table, such that their midpoints build the vertices of a regular 17-gon (regular heptadecagon) and adjacent coins touch each other. What is the ...
ThomasL's user avatar
  • 12.2k
1 vote
1 answer
137 views

How many figures to cover the kitchen floor?

The puzzle is as follows: Figure 1.1 shows a kitchen floor that is made up of 30 squares whose sides measure 1 cm in length and in Figure 1.2 a tile that is made up of 5 squares whose sides also ...
Chris Steinbeck Bell's user avatar
6 votes
1 answer
240 views

What is the name or author of this tangrams-like packing puzzle?

Does someone knows the name of this packing puzzle, or its inventor? The goal is to repack the shapes into the square with the additional red square. It is an easy puzzle but the construction is ...
pepster's user avatar
  • 156
9 votes
2 answers
471 views

Can a square of size 1000.25 fit a million and one unit squares?

A square with a side length of exactly 1000 can obviously be packed with exactly a million unit squares. If we increase the side length to 1001, then 2001 more squares can fit. But if we increase the ...
SE - stop firing the good guys's user avatar
12 votes
4 answers
792 views

A packing game!

Amy and Ben are playing a game which is suggested by a genie. Amy first chooses $a,b,c\in\mathbb{R}^+$. Then a empty cuboid box with internal measurements $a+b,b+c,c+a$, and infinite supply of cuboid ...
Culver Kwan's user avatar
  • 5,914
27 votes
4 answers
4k views

A COVID-19 puzzle: How large a class do you need to fit 30 pupils?

Some countries are proposing to reopen high schools soon. To ensure safety, they want to make sure that all pupils in a class are at least 2 m apart. To help them find the smallest room that can ...
Simd's user avatar
  • 7,845