Using Excel Solver to Find the Solution to a Geometry Puzzle

The Monday Puzzle in the Guardian by Alex Bellos had a good problem to illustrate the use of Excel Solver. The link to the article is: https://www.theguardian.com/science/2025/feb/17/did-you-solve-it-the-simple-geometry-problem-that-fools-almost-everyone.

Restated, the problem is to divide an 11 x 11 square into five rectangles so that the ten side lengths are the whole numbers from 1 to 10? 

Below is the 11 x 11 square with five rectangles and the ten sides labeled A through J. 

To use Excel Solver to find a solution, ten cells of the spreadsheet will be designated as the decision variables. In the attached spreadsheet, these are simply the cells A1 through J1. Solver will change their values until a solution is found. 

In rows 3 through 8 are 6 constraints:

A+D=11

C+F=11

E+H=11

G+B=11

H+J+D=11

B+I+F=11

Also in Solver, additional constraints are entered:

All values, A through J, are => 1 and <= 10.

All values, A through J, are integers.

All values, A through J, are different.

With these constraints entered, click the Solve button, and one of the solutions is displayed:

A=6, B=3, C=10, D=5, E=9, F=1, G=8, H=2, I=7, J=4

eleven by eleven square into 5 rectangles.xlsx

More about Solver: https://jamesmacmath.blogspot.com/2021/12/optimization-solutions-using-microsoft.html