 Solution

The hard link count in an inode duplicates information recoverable by counting directory entries that refer to its inode number. Keeping the count makes the last-name test fast: a hard link removal need not search every file-system directory. A file-system consistency checker can independently recount the references and compare the result with the stored value.

Likewise, a block allocation bitmap summarizes ownership information recoverable from allocated inodes, their file data blocks, their indirect block pointers, and reserved file system structures. This summary makes allocation efficient and supplies an independent consistency check against multiply allocated or lost blocks. Replicated superblock information is another possible form of data redundancy, helping recovery if one copy is damaged. These examples have distinct benefits: a cached count or allocation summary saves work, while an independent or replicated representation helps detect or repair corruption. Consistent updating is essential; redundancy alone does not make a file system crash-safe.