Forming Digit Equations: A Game

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It occurred to me how forming digit equations from five digits might make for an interesting game. After all, Wordle consists of guessing the five letters that make up a hidden word. In the game I'm conceiving of, a five digit number between 10000 and 99999 would be generated. Let's say the number generated is 25529. The challenge is to use only the following operators to form a digit equation without altering the order of the digits:

+    addition

-    subtraction

x    multiplication

/    divide by

|    divide into

^    exponentiation

(     left bracket

)    right bracket

Figure 1 shows one possible representation:

Figure 1

The same digit equation would look mathematically as follows:$$ \Big ( 2 + \frac{5}{5} \Big )^2=9$$This is somewhat on the difficult side. Obviously an effective game nowadays involves a catchy user interface so coloured balls that pop up to start the game would be effective. The operators shown above would need to be able to be dragged and dropped between the digits in order to generate the equation. The successful creation of an equation would need to be displayed in mathematically readable way such as was done with the example of 25529.

The game could have different levels starting at the fairly elementary level. For example, 10348 could be rendered as:$$1+0+3+4=8$$This equation involves only the a single operation, addition, and the correct placement of the equal sign. By contrast, 25529 is considerably more challenging and involves the use of brackets, addition, division and exponentiation. Of course, for some numbers it is impossible to form an equation within the imposed constraints. An example is 27497 which is unsolvable as far as I can see. This is a long term project but something that I will keep thinking about or perhaps I'll discover that someone has already created such a game. Who knows?

For earlier posts on this theme see my posts titled The Number Plate Game from the 29th June 2024 and Forming Equations from the Digits of a Number on 14th March 2024. To generate some random five digits numbers follow this permalink.