All Questions
Tagged with packing-problem puzzle
14
questions
2
votes
2
answers
226
views
Can you pack $53$ bricks of dimensions $1\times 1\times 4$ into a $6\times 6\times 6$ box?
Can you pack 53 bricks of 1×1×4 size into 6×6×6 box?
Source: puzzledquant.com
My approach: I looked at the solution and visualized the box as $3d$ checkerboard. So in total we have $27$ such $2\...
- 305
3
votes
0
answers
92
views
Maximum tiling by Y Hexomino
"Y Hexomino" has a shape as shown in the picture.
What is the maximum number of Y Hexomino that can be placed on a $13\times 13$ chessboard, where each Hexomino does not overlap?
From the ...
- 183
0
votes
1
answer
149
views
2D packing problem, as a puzzle.
I have discovered a 2D packing problem that I cannot find the tools online to solve, so I have decided to present it to the Mathematics Stack Exchange as a fun puzzle.
In this problem there exist 4 ...
5
votes
0
answers
228
views
Articles from the Journal of Recreational Mathematics from the 1970s
When reading some articles about packing puzzles I regularly stumble accros references from the "Journal of Recreational Mathematics" from the 1970s. I did not found any way of accessing ...
- 649
5
votes
2
answers
830
views
Number of plates that can be placed on the table so that they neither overlap each other nor the edge of the table?
Table in my room is round in shape and its radius is 15 times the radius of our plates, which are also round in shape. Find the number of plates that can be placed on the table so that they neither ...
- 388
0
votes
1
answer
238
views
How many balls can fit in a house shaped box?
Consider the following house shaped box with the indicated measures:
I need to get the best possible approximation of how many balls of 3 inches of diameter can fit in this box without exceeding the ...
- 2,446
0
votes
0
answers
69
views
Help with understanding if my way to solve the riddle works or not
So the riddle i was asked is:
you have a circle, with a radius of 9,
prove that you cant pack 101 points inside of it, without having at least a pair of dots with a distance less than 2 between them.
...
3
votes
1
answer
126
views
Tiling a room when (room and/or tile) dimensions are irrational
My question is inspired by this question.
There is a rectangular room of dimension $a \times b$, and there is an unlimited number of rectangular tiles of dimension $c \times d$. You are allowed one ...
- 15.4k
1
vote
3
answers
518
views
Minimum number of trips for a truck with weight limit of $200$ to transport boxes with weights 81, 73, 67, 49, 37, 34, 30, and 26
My 9-year-old son had the following math problem to solve:
A truck can carry $200$kg or less. We have 8 different boxes with given
weights:
$81$kg, $73$kg, $67$kg, $49$kg, $37$kg, $34$kg, $30$kg, and ...
- 131
3
votes
2
answers
748
views
maximal minimum distance between points in a rectangle of size $17\times 32$
I am training in problem solving and this one greatly resists to my understanding:
Given a rectangle with specified length and width, you have to place 5 points in the rectangle such that you ...
user386721
6
votes
1
answer
388
views
Inequality AM/HM <= (AM/GM)^n with packing problem interpretation
I have stumbled upon the following inequality while exploring "Hoffman's packing problem", which I'm pretty convinced is true, but unable to prove. Let $n \geq 2$ be a natural number and let $x_1, \...
- 179
6
votes
3
answers
257
views
How many $9\times 9$ squares can I cut from this figure (it's $40\times 38$ without some corners)
Can I cut 16 ones (along the grid)?
I've tried to paint some $15$ cells so that every $9\times 9$ square contain only $1$ painted cell (so I prove there can't be $16$), but to no avail.
The figure (...
- 5,236
21
votes
1
answer
2k
views
Why are these geometric problems so hard?
I was surprised to learn that both for the Moving Sofa Problem and Packing 11 Squares solutions have been proposed, but in either case the optimality of the proposed solution is, as of yet, only ...
- 3,220
8
votes
1
answer
1k
views
Finding the maximum number of $70\times 30$ tiles that can be placed into a $110\times 130$ floor, without trial and error
The following question was asked in a competitive exam
Rectangular tiles each of size 70 cm by 30 cm must be laid
horizontally on a rectangular floor of size 110 cm by 130 cm, such
that the tiles do ...
