Number Daisy

1 = 1 2 = 2 3 = 1 + 2 4 = 4 5 = 5 6 = 2 + 4 7 = 1 + 2 + 4 8 = 5 + 1 + 2 9 = 4 + 5 10 = 7 + 1 + 2 11 = 5 + 4 + 2 12 = 5 + 4 + 2 + 1 13 = 7 + 6 14 = 7 + 6 + 1 15 = 7 + 6 + 2 16 = 7 + 6 + 2 + 1 17 = 7 + 5 + 4 + 1 18 = 7 + 5 + 4 + 2 19 = 7 + 5 + 4 + 2 + 1 20 = 5 + 7 + 6 + 2 21 = 5 + 7 + 6 + 2 + 1 22 = 4 + 5 + 7 + 6 23 = 5 + 7 + 6 + 1 + 4 24 = 5 + 7 + 6 + 2 + 4 25 = 5 + 7 + 6 + 2 + 4 + 1	This is a special Daisy because you can make all the numbers from 1 to 25. You are only allowed to add neighbours (numbers touching each other) and you can only use one of each number in a sum.

We can make all the numbers from 1 to 25 using this Daisy.
Can you do better than this with a different set of numbers?
The challenge is to find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25.
 

This task was found in one of Brian Bolt's books and developed by MEDIAN in their collection of interesting number resources.