Consider this image below.
Its a magic hexagon using repeated digits to create a magic sum of 10.
All rows columns and diagonals, meaning the cells in any straight line through the hexagon in any direction will sums to 10.

Because some lines through the hexagon have 3 cells and some have 4 cells and some have 5 cells. Filling the grid with all 1s will not produce a magic total with everything summing to the same number.

magic hexagon using repeated digits

What is the smallest magic sum that is possible where all direct lines through the grid have the same sum.?
Repeated digits are allowed.
Is the above image the smallest?


2 Answers 2


My answer for the least sum along any line is

sum = $8$

enter image description here

  • $\begingroup$ Assuming we're not using 0, I think this is minimal. I found almost the same solution, just using 2,3 instead of 1,4 in the corners. Using zeros the sum can be 2. $\endgroup$ Mar 9, 2023 at 21:49
  • 3
    $\begingroup$ @JaapScherphuis using all zeros the sum can be 0 :) I think you should post your solution, as it uses smaller values to reach the same sum. $\endgroup$ Mar 9, 2023 at 22:09

smallest solution

I believe this is the smallest value of n using the smallest digits


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