Four Rules, factorial

Students can find the first two challenges a welcome activity, where they have the freedom to find their own means of generating the Four Fours terms. The First Challenge provides use of the four rules + – x ÷, and the factorial can be dropped in ahead of time if necessary. Starting students on a blank Four Fours puzzle can help them practice evaluation of mathematical expressions using the BODMAS rule, and other operators such as ! (factorial), power, and square root.

Analytical techniques, more operators

The towards the Second Challenge, there comes an awareness of building blocks using 1, 2, or 3 fours, and re-using them with other blocks for building other solutions, e.g. using 4!–4 to obtain 20, then using 4/4 with + and – to obtain 19 and 21.

Programming

Undergraduate computer science and mathematics students might benefit from partaking in a project that finds Four Fours solutions. Techniques that can be used: expression parsing, dynamic structures, recursion, algorithm complexity, and interface design.

Attempts to meet this challenge are found in the Four Fours Links page.

Mathematical computing

Try to find a means of determining whether a solution exists for any given number, without using a look-up to a table of complete Four Fours solutions, and without resorting to an exhaustive combinatorial analysis.