378. Missax [ Easy | 2026 ]

Score: ★★★★½ (out of 5)

Missax is a compact, artful experiment that rewards patience and curiosity. If you have an hour and a half to spare, a good pair of headphones, and a willingness to listen—to both the music and the story—press start. You might just leave the void feeling a little less alone.

Further Reading & Resources

Thanks for joining me on entry #378. Stay tuned for the next numbered adventure—who knows what hidden gem awaits at #379?

If you’ve ever played Journey or Proteus, you’ll recognize the power of a dynamic soundtrack. Missax takes that a step further: each puzzle solution adds a layer, rather than merely changing a preset track. By the final node, you’ll have built a unique, player‑specific composition—a sonic representation of the narrative you’ve assembled. 378. Missax

The sound design also uses spatial audio (if you have headphones), making the faint echo of distant notes feel like they’re emanating from the void itself, reinforcing the feeling of isolation and introspection.

We prove by induction that after processing the first (i) elements ((i\ge 1)):

Invariant 1. curSum equals (\textbest_ending_i).

Invariant 2. maxSum equals (\displaystyle\max_1\le j\le i \textbest_ending_j). Score: ★★★★½ (out of 5)

Invariant 3. start is the leftmost index (l) of a subarray achieving curSum.

Invariant 4. bestL, bestR delimit a subarray achieving maxSum.

Base case ((i=1)).
curSum = maxSum = A[1]. By definition (\textbest_ending_1 = A[1]) and the maximum over the first element is also (A[1]). start = bestL = bestR = 1. All invariants hold.

Inductive step. Assume the invariants hold after processing index (i-1). Consider element (a_i). Missax is a compact, artful experiment that rewards

Thus, by induction, all invariants hold after processing the entire array. At termination maxSum equals (\displaystyle\max_1\le l\le r\le n\sum_k=l^ra_k), i.e., the desired answer, and bestL, bestR delimit a corresponding subarray. ∎

| Teaching Point | How 378 Illustrates It | |----------------|------------------------| | Retro‑grade promotion | The missing queen appears on a back‑rank square that could only be reached via promotion, prompting solvers to think “which pawn could have become a queen?”. | | Castling‑rights deduction | The presence of a piece on e8 immediately tells us that Black’s castling rights are gone, a subtle clue that many beginners overlook. | | Material‑balance audit | By counting pieces before and after inserting the missing piece, students practice the vital skill of “does the capture history make sense?”. | | Minimalism | Only one piece is missing, yet that piece resolves three independent constraints—perfect for illustrating the elegance of Missax design. |

Books, especially in genres like science fiction, mystery, or fantasy, often use codes, numbers, or unique identifiers as titles or within their narratives.