Hi Bobby,

Yes, 41 is possible: 8 + 17 + 12 + 4 = 41

Here's how I got them all:

I used T&E to find the six numbers.

I think 1, 2, 4 & 8 are essential for the first four numbers, and a central 1, surrounded by 8 > 2 > 4, gives the highest score: 11.

So that gives 12 (or something lower) for the fifth number.

12 succeeds right up to 19, and I then tested for the sixth number, starting with 28 (one greater than the sum of the other numbers) and working down. 17 is the first one that works up to the sum of all six numbers.

I doubt that number 1 would succeed anywhere but in the centre, as probably all the other numbers need access to it at some stage or other, which would not be possible if it were placed on the outer ring.

I wonder what the max is.