##
Fibonacci Dials

Can you create a set of dials that meet the following requirements?
- There are six dials, each with four values. Each value is a unique
positive integer (for a total of 24 unique values.)
- The dials are arranged left to right. The first two dials spin
freely. The other dials may only turn to a new value if the two
previous dials sum to that value.
- There are no unused values. There exists some way for each dial to
turn to all four of its values, and the values on the first two dials can
all be used in a sum. (The first dial's values can all be used with
values from the second dial to obtain a sum on the third dial. The
values on the second dial can be used to obtain a sum on either the third or
fourth dial. For example, the first three dials could be: {1,2,3,4};
{5,6,7,8}; {9,10,11,12}. The {1,2,3,4} can be summed with {8,7,6,5} to
obtain "9" on the third dial, and the {10,11,12} can all be obtained through
other sums.)
- The largest value (of all 24) is as small as possible.

Source: Original.

Solution

Mail to Ken