Source file: mathPuzzle.py

This program came about from a math puzzle given to me by a friend. The problem comes from the book "Hacking: The Art of Exploitation, 2nd Edition", by Jon Erickson. The basic premise is this: with the numbers 1, 3, 4, and 6 as well as the four basic math operations (add, subtract, multiply, divide), how can you get 24? Each number can only (and must be) used only once, and operations can be used in any order/repetition.

After being unable to solve the problem by hand (or in other words, without the help of a computer), I was intrigued by the idea of attempting to write a program to do so. The idea of the solver is that for any given solution, there will be some combination of the four numbers (1, 3, 4, or 6), and some combination of three operations (+, -, *, /). For example, 1*3+4/6 is a potential solution.

However, this set of solutions is much too simplistic, and cannot possibly form the correct solution. When doing math in our heads, we do not think explicitly placing parentheses in front of or after numbers (most of the time), because we can either think through the operations in a certain order, or write out an expression in a form a computer cannot. Therefore, there are eight additional operations, ( +(, ..., )+, ... ) where ... represents the other three operations with similar parentheses placement. This allows for something like 4*(3-1)+6 to be checked as a solution as well.

Next, it is one thing to have an idea, but to implement it in code then takes another level of understanding. The premise of my solution method was based on a brute force method, meaning check every possible combination available until a solution is found. For this, I needed a few tools from the itertools library (see documentation here). With the four numbers, only unique combinations needed to be checked, so an iterable was generated using the method permutations. With the operations, repeats are allowed so all combinations needed to be checked, giving rise to the use of the product method for Cartesian Product. Although both are interesting discussions on their own, I will not go into the details here.

Finally, this program makes use of the built-in eval() method. In showing this program to other Python users, I was suprised to find that many were not aware that eval() can evaluate a string as a mathematical expression. For example, the line eval('4+2') would give an output of 6. Utilizing this, I was able to build mathematical expressions using strings in a loop structure (looping through both sequences of numbers and combinations of operations), and then evaluate each expression using eval().

Overall, writing this solver was a new experience that taught me more about working with strings, and more generally gave me a new perspective on ways I could utilize Python. In writing code, creativity and cleverness is very important, and this was a fun and challenging exercise in both of those skills.

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