What is the optimal way to divide a picture into jigsaw puzzle pieces?

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Discussion Overview

The discussion revolves around the optimal way to divide a picture into jigsaw puzzle pieces, focusing on the dimensions, proportions, and total number of pieces. Participants explore various configurations and mathematical approaches to achieve aesthetically pleasing piece shapes while adhering to specified constraints.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant outlines the project parameters, including image dimensions and desired piece count, and expresses uncertainty about the method to achieve the goal.
  • Another suggests using the total piece count of 96, which is divisible by 6, to find suitable row and column configurations through prime factorization.
  • A later reply reiterates the approach of solving for rows and columns but expresses confusion regarding the calculations.
  • One participant identifies a few valid combinations for piece counts and proportions after refining their parameters.
  • Another proposes a method to calculate tile dimensions based on the desired number of pieces and their proportions, leading to a specific configuration of rows and columns.
  • One participant reflects on the flexibility of the piece count and finds a configuration that yields a pleasing shape, although they acknowledge a mistake in their calculations.
  • There is a discussion about the necessity of having at least two factors for the number of pieces, with some participants confirming the factorization of specific numbers.
  • Participants mention practical considerations, such as sourcing materials for the puzzle and the challenges of printing the pieces accurately.
  • Links to external puzzle-making services are shared, indicating interest in commercial options for creating large puzzles.

Areas of Agreement / Disagreement

Participants express various approaches to dividing the image into puzzle pieces, with some agreeing on the mathematical methods while others question the calculations. There is no clear consensus on the optimal configuration, and multiple competing views remain regarding the best way to achieve the desired outcome.

Contextual Notes

Participants note limitations in their calculations and assumptions about piece dimensions and proportions, which may affect the validity of their proposed solutions.

DaveC426913
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I've got this project that I'm having trouble pinning down.

I'm cutting a pic up into squares to make a sort of jigsaw puzzle. I want the pieces to be a pleasing shape and the number of pieces to be within a small range.
- proportions of pic: 3:2 (so, say 6000 wide by 4000 high) this is slightly variable by a small amount, say < 5%, if that makes the numbers work
- total number of pieces: between 80 and 96
- proportions of pieces: between 1:1 and 2:3 (so, say 600 wide and 800 tall)
Not that the pic is horizontal but the pieces are vertical.

If I used the example dimensions, I get 6000/600 by 4000/800 = 50 pieces, which is too few.

Not sure how to do this except by brute force.
 
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You could select a piece count of 96 because its divisible by 6 ie 2x3 and then find its prime factors.

From there solve 2x* 3y=96 where x is rows and y is columns or vice versa.
 
jedishrfu said:
You could select a piece count of 96 because its divisible by 6 ie 2x3 and then find its prime factors.

From there solve 2x* 3y=96 where x is rows and y is columns or vice versa.
Not sure I follow.
If y=8 then x would have to be 12.
So, each piece would be 24x36?
 
I guess, now that I've clearly defined my required parameters,
- number = 80 to 96,
- proportions between 1:1 and 1.5:1 (vertical),
there's only a very few valid combinations.
6x14..84..667x429..1.55:1
7x12..84..571x500..1.14:1
7x13..91..571x462..1.24:1
8x12..96..500x500...1:1
 
Last edited:
The idea was to take your 4000 x 6000 image and to say its ratio is 2 by 3 and you want to tile it with say 96 tiles

so it has a tile area of 96 with one side being 2x units and the other side being 3y units hence the 2x * 3y = 96

which then leads to x * y = 16 and from there the squarest choice is x = y = 4

this then give 2x = 8 tile units by 3y = 12 tile units

which means you slice your image up into 8 rows by 12 columns and you'll have 96 pieces to play with.
 
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Thanks. Although I think that's approaching it from the other end, now that I try it.

The number of pieces is flexible, between 80 and 96.
If I wanted a pleasing shape for the pieces, the 7x13 gives me a 1.4:1 . That's 91 pieces.
I'd have to do 13x*7y=91, which simply gives me the unit 1.

Hm. I've done something wrong there. I've misused the formula.

Though I'm pleased with the answer. 91 pieces in a 5:4 proportion.
 
Doesn't the number of pieces have to have at least two factors? I could see 90 but not 91.
 
jedishrfu said:
Doesn't the number of pieces have to have at least two factors?
Yes. 7 and 13.

WeddingPartygrid.jpg


So, I throw away the border, with no useful information for assembly.
Still, a lotta squares with just black in em... :smile:
And ther "nothin-but-curtain" squares above the rather diminutive bride.

It seems Curry's Art Store sells sheets of 3/16" foam core in 48"x96" sheets for $16 (frankly sounds too good to be true).

I could make this thing 8'x5'4" with each piece being 7.4"x9.1" (so that's ... 63dpi).

The next tricky part is going to be sizing and printing each image piece out so that it registers with the next one.
 
Last edited:
  • #10
  • #11
Oh 8 feet wide, I see what you mean!
 
  • #12
MrAnchovy said:
Oh 8 feet wide, I see what you mean!
There's a Spinal Tap joke in here somewhere. :biggrin:

spinal_tap_stonehenge.jpg
 

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