Can you replace the letters with 10 consecutive primes such that the sum of numbers on each line is equal? I expect this to be solved with a computer.

Good luck!

enter image description here

  • 5
    $\begingroup$ Is there any method to solve this besides trial and error? $\endgroup$
    – Deusovi
    Oct 13, 2019 at 2:35
  • 5
    $\begingroup$ For the record can you please stop criticizing every puzzle I post. Yes I like mathematical puzzles and some of them require a bit of trial and error. I don't see anything wrong with that. Also I think it is ok to solve puzzles with a computer. In fact there are some very clever algorithms that allow you to reduce the search space and find the solution faster. For me coding/developing such algorithms is part of the fun, especially if you can use them to solve larger cases and push the boundaries of your knowledge. $\endgroup$ Oct 13, 2019 at 2:43
  • 5
    $\begingroup$ I like mathematical puzzles too. But for something to be a puzzle, it should permit a clever "aha moment" that leads to the solution. What makes a good puzzle is a "path" to the solution, somehow "built into" the puzzle. Questions that require large amounts of trial and error don't satisfy that, in my view. $\endgroup$
    – Deusovi
    Oct 13, 2019 at 2:45
  • 6
    $\begingroup$ Your "Paint 7 cells of a 7x7 grid" had a very nice path to the solution (though I don't know whether it was intended). But I'm critical of this (and similar puzzles) because I don't think it has an "aha moment", or a natural "path" to the solution. If the intended way to solve something is brute-force search (or mostly brute-force search), I don't think it's very good as a puzzle. It may be a great programming challenge for a site such as Project Euler, but that does not make it a puzzle. $\endgroup$
    – Deusovi
    Oct 13, 2019 at 2:51
  • 5
    $\begingroup$ I agree with @Deusovi on this one, as manually solving it is practically impossible. If you intended for this to be solved with a computer, you should say so and present it as a coding challenge. As it is, one might expect to find a solution in small primes. Woe unto them. $\endgroup$ Oct 13, 2019 at 3:04

1 Answer 1


First, this image shows examples of translation that preserves the summed groups. As mentioned in comment, there are $12$ equivalent arrangements in this class.


Here is a solution set:


There are seven other solution sets with primes less than 100,000 and countless more with larger primes.

  • $\begingroup$ You got it! The first answer had a bug, but this one is correct. Feel free to post other solution sets. $\endgroup$ Oct 13, 2019 at 21:45

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.