Fifty books belonging to different subjects history, geography, literature, psychology, and science are placed on a shelf to arrange in alphabetical order, subject to the condition that no books of the same subject are placed together so long as the books of other subjects are available. All counting is done from the left.





The first step is to categorize the books based on their subject. We have five subjects - history, geography, literature, psychology, and science. We can arrange the books in the following way:

- History: H1, H2, H3, H4, H5
- Geography: G1, G2, G3, G4, G5
- Literature: L1, L2, L3, L4, L5
- Psychology: P1, P2, P3, P4, P5
- Science: S1, S2, S3, S4, S5



Now that we have categorized the books, we can start arranging them. We need to make sure that no books of the same subject are placed together so long as the books of other subjects are available.

We can start by arranging the books of the first subject, which is history. We can arrange them in alphabetical order, which means that we will have:

- H1, H2, H3, H4, H5

Next, we need to arrange the books of the other subjects. We can start with geography and arrange them in alphabetical order. However, we need to make sure that no books of the same subject are placed together so long as the books of other subjects are available. This means that we cannot place G1 after H5 because it would be the same subject as G2, which is the next book. Therefore, we need to place G1 after H4. We can arrange the rest of the geography books as follows:

- H1, H2, H3, H4, G1, G2, G3, G4, G5, H5

Next, we need to arrange the literature books. We cannot place L1 after G5 because it would be the same subject as L2, which is the next book. Therefore, we need to place L1 after G4. We can arrange the rest of the literature books as follows:

- H1, H2, H3, H4, G1, G2, G3, G4, L1, L2, L3, L4, L5, G5, H5

Next, we need to arrange the psychology books. We cannot place P1 after L5 because it would be the same subject as P2, which is the next book. Therefore, we need to place P1 after L4. We can arrange the rest of the psychology books as follows:

- H1, H2, H3, H4, G1, G2, G3, G4, L1, L2, L3, L4, P1, P2, P3, P4, P5, L5, G5, H5

Finally, we need to arrange the science books. We cannot place S