Finding a System of Distinct Representatives (SDR) for Sets s1={5,6}, s2={3,6}, s3={4,5}, s4={2,3}, s5={1,2}, s6={1,4}

To find an SDR for this system, we can use the following algorithm:

1. Start with the first set in the system (s1={5,6}).
2. Try to find a set that intersects with s1 in exactly one element. In this case, s4={2,3} intersects with s1={5,6} only at element 3.
3. Add s4 to the SDR.
4. Repeat steps 2 and 3 for the remaining sets until all elements are covered or no more sets can be added.

Using this algorithm, we can construct the following SDR:

{5,6} from s1 {2,3} from s4 {1,4} from s6

This SDR covers all elements in the system exactly once. Therefore, the system has an SDR.

Note: There may be other SDRs for this system, but the above algorithm guarantees finding at least one SDR if it exists.