# Tag Info

Accepted

They are:
• 13.6k

### Social distancing in a 5x5 room

The problem is equivalent to Now,
• 28.1k
Accepted

### Social distancing in a 5x5 room

I'll get things started with:
• 14.4k
Accepted

### 12 piece cube packing puzzle

What a great puzzle! For me the key was to notice that you will quickly run out of corners. Since there is only one other way (plus a zillion symmetries) to place the hexacube, this means that we ...
• 78k
Accepted

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

The solution that springs to (my) mind is to put them
• 28.1k

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

As in my answer to My Mother's Dish Collection, I used a nonlinear optimization solver, with variables $x_i$, $y_i$, $w$, $h$. The problem is to minimize $w\cdot h$ subject to: \begin{align} 0 \le ...
• 14.4k
Accepted

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

The trick to this puzzle is to: (And here are those tilings: the center was already given, and the rest are obtainable from these by rotation.)
• 148k

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

With integer programming, I managed to place like this. Here is my formulation. I happened to solve a similar model to solve a puzzle called One puzzle a day. Let $B$ be the set of cells in the 8x8 ...
• 525

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

I solved this completely by hand. Here is a clean proof of its optimality. No computer is needed. Mere pencil and paper suffice. Expand each pentomino by adding little right-angled isosceles ...
• 1,236
Accepted

### Packing pentominoes in a circle

UPDATE 2 A minor improvement. New best radius Arrangement /UPDATE 2 UPDATE New best radius: using arrangement /UPDATE I get a radius of about using the following scheme which is obviously ...
• 21.3k
Accepted

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

It is because Thanks to mousetail in the comments, here is a picture:
• 54.2k

### Smallest rectangle to put the 24 ABCD words combination

Pretty sure that the following is minimal.
• 261
Accepted

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

I used a computer to search for all solutions, and the number of solutions is Here is a picture of the solutions, with the top layer on the left, bottom layer on the right.
• 54.2k
Accepted

### Can you stop the falling piano with 23 nets?

One straightforward way to arrange the nets for question 1 is as follows: Number the poles $0$ to $22$. Here are some thoughts on question 2:
• 54.2k
Accepted

### 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

Yes, for instance we can make a 2x7x15 block. Put together two pentacubes to make a P pentomino two layers deep: Then, arrange 21 P pentominoes in 2D to make the 7x15 rectangle below. Image from ...
• 27.4k
Accepted

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

I've been able to do it in You have to arrange the reindeers like this I found it by generating and evaluating all possible arrangements. It feels like a really good solution, but I cant proof if ...
• 206

### Packing pentominoes in a circle

I can get a radius of: Method: start with and then EDIT: I found a second solution with the slightly worse radius Method: start with and then I found both of these with the help of

5x5x5 block:
• 5,364

### Ten tetrominoes inside an 8x8 grid

what about the following arrangement of I found it manually by searching arrangement of same pieces, then had to change a bit strategy
• 1,484
Accepted

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

Here's one solution for the $10{\times}6$ rectangle: Here are all $11$: ...
• 5,364
Accepted

### Cutting a square into integer triangles

An optimal 26-triangle solution: Previous manual construction of a solution with 25 triangles: GeoGebra construction to confirm validity:
• 15.4k
Accepted

### Packing 25 three-dimensional N pentominoes into a 5x5x5 cube

You can solve the problem via integer linear programming as follows. For each of the $960$ placements $p$ of a piece, let $C_p \subset [5] \times [5] \times [5]$ be the set of cells covered by $p$, ...
• 14.4k

### Is this more than a packing puzzle?

A small addition to phenomist's excellent answer: Finally, here's a photo of all the pieces in the box. The tricky packing isn't visible.
• 2,737
Accepted

### Eighteen is not seventeen

Not a perfect circle, but it is clear that it works, and I didn't use a computer:
• 14.4k

### Dividing a piece of land

Alice can maximize her area by Why? Increasing the number of points will only decrease Alice's area because There are a few other things Alice can try: Reference:
• 1,334
Accepted

### Put three pieces of cake into a round box

An "improved" version of AxiomaticSystem's solution: PS: I realize the layout is actually the same as AxiomaticSystem, an optimal $\theta$ will put the more acute angle at the bottom as I ...
• 30.9k
Accepted

### Multi-colored polyominoes inside a 7x7 grid

I think this would work as a possibility
• 138k

### Multi-colored polyominoes inside a 7x7 grid

Here is a solution in which the red and green do not touch.
• 54.2k

Hint Solution:
• 9,366