So, there is a hexagonal grid made up of 19 circles (see attached image). The objective is to arrange the numbers 1 to 19 on the circles so that, in any direction of the lines, the sum of the numbers is the same. Problem is, I'm having trouble figuring out what the sum should be - anyone know how I would go about determining this sum?

If you look at the rows that are seperate from each other, there are five in each direction. Therefore the sum has to be 1/5th of (1+2+...+19), or 38.

that's incorrect, there are 15 lines, so that would make the average


…12.6??


EDIT - it's not 12.6 because the numbers are used more than once to add, so you can't just take the average of them or divide them by the number of lines

But there are 5 numbers per line. Kyle90 is right. The total per line should be 38.

what do you mean by 5 numbers per line? the top row only has 3 and the row next down has 4.

sorry, i mean 5 numbers on the longest line.

ah I see. I just found 38 a different way:

Each circle affects 3 lines, the horizontal and the two verticals that it lies on. Therefore each number counts 3 times. 190 * 3 is 570, and that divided by the number of lines in the hexagon(15) = 38. It's the same answer with an extra STEP

190 / 5 = 38
19 * 3 / 15 = 38

I still don't understand how saying the center line has 5 numbers and dividing the total by 5 will get you 38, but as long as we have the same number it doesn't matter.

38 is correct. This thing is called a magic hexagon, in case anyone wants to look it up.

someone'll probably post an answer they found online but I'm still going to try and solve it. I usually work on these things for about 5 minuntes, get bored and go play CS

EDIT - **** this game. I looked up the answer online and you can do it with complicated mathematical equations. I guess I was right about the above stated :/