Hint 1 : Remember, we need nice simple ratios between any two strings in your scale.

For example 5/9 of the unit would probably sound good with Note 1 and 6/7 would also sound OK with Note 1, but 5/9 and 6/7 would probably not sound good together because their length ratio (35:54) is not simple.

Hint 2 : Once you have the ratios for all your strings - you should be able to show that taking any pair of strings, you only once have a ratio with numbers bigger than 10.

Hint 3: You have ratios based on halves and thirds - what else could you try?