Tips & Tricks for how to solve matchstick puzzles when you’re stuck, without needing a full solution.
- Some puzzles must be solved by moving exactly N sticks. If you’ve found a solution that wins in less moves, don’t despair – you can turn it into a “valid” solution by wasting intermediate moves.
… Other than that, I don’t actually have any clever tips for how to solve sum & product matchstick puzzles, to the point that I got quite frustrated with the game. But I found a solution, via the Power of Spreadsheets.
Since I couldn’t find a way to solve the puzzles in clever ways, the next-best thing was to use a brute-force method to find a shortlist of valid puzzle solutions.
Almost all puzzles in the game are sums, subtractions, products or divisions of three 1-digit numbers, e.g. A + B = C or A * B = C.
When such a formula is written in matches, each figure requires a different number of matches, e.g. a figure “1” requires 2 matches, whereas a figure “0” requires 6 matches.
In this game, you can always determine exactly how many matches are required in a puzzle.
For instance, say you have a sum puzzle of the form A + B = C, to be solved with exactly 14 matches.
It turns out that such a puzzle only has three valid solutions (assuming A<=B): 0+4=4, 2+2=4, 2+7=9.
Once you know that, it makes solving the puzzle much, much easier.
But how would you know that a 14-matchstick sum puzzle only has three available solutions? Simple – I’ve made a spreadsheet which you can find below.
… and how to use them
How to use these spreadsheets or tables:
- Confirm that you’re solving a 3-figure sum, subtraction, product or division, e.g. A + B = C or A * B = C. The tables cannot be used to solve more complex formulas like A + B = C^2.
- Determine the number of matches required in the puzzle. Count the available matches. In Move puzzles, that’s it. In Remove puzzles, you’ll have to subtract the number of matches to remove. And in Add puzzles, add the number of matches to add.
- For sums and subtractions, consult the Sums table. The table is formatted in the form Summand 1 + Summand 2 = Sum, which corresponds to A + B = C. It assumes A <= B, but in-game A and B can be flipped around. For subtractions, the formula is C – B = A or C – A = B, so Sum is your left-most figure, and Summands 1 and 2 are your middle and right-most figures.
- For products and divisions, consult the Products table. The table is formatted in the form Factor 1 * Factor 2 = Product, which corresponds to A * B = C. It assumes A <= B, but in-game A and B can be flipped around. For divisions, the formula is C / B = A, or C / A = B, so Product is your left-most figure, and Factors 1 and 2 are your middle and right-most figures. For divisions, you can ignore any situation that would require you to divide by zero.
- In whatever table you’re consulting, find all the rows where “number of matches” equals the number of matches you have available. These are the entire list of potential solutions; there are no others.
Table of Sums
A prettier version of this ugly BBCode table can be found here – [google.com] . Steam will warn you that it’s a potentially malicious URL, but it’s just a Google Sheet.
|Summand 1||Summand 2||Sum||Number of matches|
Table of Products
A prettier version of this ugly BBCode table can be found here – [google.com] . Note that you’ll have to manually navigate to the Products sheet.
|Factor 1||Factor 2||Product||Number of matches|
If you found this guide useful, I’d love to hear so from you! Creating guides takes time which could be spent on other things, after all :).
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