Go with the heat flow

Find the solution to a sudoku puzzle such as the one below.

 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 1 2 3 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 9 1 5 6 7 8 9 1 2 3 4 8 9 1 2 3 4 5 6 7 3 4 5 6 7 8 9 1 2 6 7 8 9 1 2 3 4 5 9 1 2 3 4 5 6 7 8

Make two copies of the puzzle answer.

Use a pencil to shade in each square of the puzzle based on the number in the square.

The higher the number the darker you should shade each square.

Shade a square that contains the number 9 to black, leave 0 white, and shade 5 gray.

Next starting at the upper right break the puzzle into squares that are 3 cells wide and 3 cells high.

for the top left 3x3 this is

 1 2 3 4 5 6 7 8 9

In this square average all of the numbers, that is sum them all up then divide by 9. Do this for every 3x3 square in the puzzle.

with an average of (1+2+3+4+5+6+7+8+9)/9 = 45/9 = 5

Now shade the 3x3 squares in the same way you did above.

What do you see?

Try this with other Sudoku puzzle answers.

Here is a puzzle. The goal is to fill every row with each of the integers from 1 through 9, every column and every 3x3 square.

Here is its solution

So What?

If each number is thought of as a temperature, in time heat will flow from hot regions to cool regions after a long time, if the square is insulated from its surroundings the square will reach a uniform temperature.

Copies of Sudoku

 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 1 2 3 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 9 1 5 6 7 8 9 1 2 3 4 8 9 1 2 3 4 5 6 7 3 4 5 6 7 8 9 1 2 6 7 8 9 1 2 3 4 5 9 1 2 3 4 5 6 7 8

 1 2 3 4 5 6 7 8 9 4 5 6 7 8 9 1 2 3 7 8 9 1 2 3 4 5 6 2 3 4 5 6 7 8 9 1 5 6 7 8 9 1 2 3 4 8 9 1 2 3 4 5 6 7 3 4 5 6 7 8 9 1 2 6 7 8 9 1 2 3 4 5 9 1 2 3 4 5 6 7 8

 Scientific Explorations with Paul Doherty © 2007 1 November 2007