Final answer:
The youngest star cluster can be identified by analyzing its H-R diagram, with the most spread out cluster in terms of brightness and temperature being typically the youngest due to the presence of hot, bright, massive stars.
Step-by-step explanation:
To determine which star cluster is the youngest, one can look at the distribution of stars in a Hertzsprung-Russell (H-R) diagram, where the stars' brightness is plotted against their surface temperature. Young clusters tend to have many hot, bright, massive stars and show significant spread in the diagram because such stars have not had time to evolve away from the main sequence. Older clusters have fewer hot, massive stars and tend to have stars that have already evolved off the main sequence, typically making the cluster look less spread out.
By simulating (or observing) and analyzing the spread and position of stars in the clusters on the H-R diagram, one can infer the relative ages of the clusters. The cluster that is most spread out in both brightness (up and down) and temperature (left and right) would typically be the youngest, because it would contain more stars that are still in the early stages of their life cycles, burning brightly and at high temperatures.