The Sandstone Smuggler

The three trucks carry 16, 6, and 2 crates respectively. Verification: 16+6+2 = 24 ✓, 16×6×2 = 192 ✓, all distinct ✓. Constable Preethi should prioritise searching the truck carrying 16 crates.

Set up the system: a+b+c = 24 and a×b×c = 192 with a > b > c > 0, all distinct integers. Factorise 192 first, then search through factor triplets for those summing to 24. Step 1: Factorise: 192 = 2⁶ × 3 = 64 × 3. List its factor triplets (where each factor ≥ 1): (1,1,192), (1,2,96), (1,3,64), (1,4,48), (1,6,32), (1,8,24), (1,12,16), (2,2,48), (2,3,32), (2,4,24), (2,6,16), (2,8,12), (3,4,16), (3,8,8), (4,4,12), (4,6,8). Step 2: Check sums: (1,1,192) → 194. (1,2,96) → 99. (1,3,64) → 68. (1,4,48) → 53. (1,6,32) → 39. (1,8,24) → 33. (1,12,16) → 29. (2,2,48) → 52. (2,3,32) → 37. (2,4,24) → 30. (2,6,16) → 24 ✓ Step 3: Triplet (2, 6, 16): 2+6+16 = 24 ✓. 2×6×16 = 192 ✓. All distinct ✓. Ordered: 16 > 6 > 2. Step 4: Continue checking remaining: (2,8,12) → 22. (3,4,16) → 23. (3,8,8) → 19 (not distinct). (4,4,12) → 20 (not distinct). (4,6,8) → 18. Step 5: Only (2, 6, 16) satisfies both constraints with all distinct values summing to 24. Step 6: Constable Preethi should search the truck with 16 crates first — the largest load, most likely to contain the hidden sculptures. Key Insight: Factor triplet enumeration is the key technique. By listing all factor triplets of 192 and computing their sums, you avoid algebraic manipulation that can get messy. Uniqueness of the solution means the smuggler's distribution is unambiguous — a satisfying closure for the story.