Case 43 · letter ordering · Easy · About 6–9 minutes
A tailor is stitching six different letter patches into a single straight seam. Before the cloth is folded, she copies down relationships between neighboring patches. The six patches later fall loose, but the notes survive.
Rebuild the seam from those relationships. Recognizing an English word can confirm your result, but it is not one of the rules you must assume.
The patches are T, I, N, S, E, L. Use each patch exactly once in six positions, read from left to right.
The tailor’s notes say:
- I is immediately before N.
- N is immediately before S.
- E is immediately before L.
- L occupies the last position.
- T occurs somewhere before I.
What six-letter string do the patches form?
“Immediately before” means the positions are adjacent, with no intervening patch. “Somewhere before” need not mean adjacent. The line has a beginning and an end; it is not a necklace whose last patch connects around to the first.
No patch may be turned into another letter, reused, or removed. There are no spaces in the result. All five notes are true at the same time. The arrangement in the supply list is simply the list of available patches and is not an extra order constraint.
Hint 1 - reveal when you want a nudge
The first two notes combine into a single three-letter block. Do not arrange I–N and N–S as though they used two different N patches.
Hint 2 - reveal when you want a nudge
The blocks are INS and EL. L must be last, so EL occupies positions 5 and 6. Consider where T can go in the four remaining positions.
Reveal the solution and explanation
The seam reads TINSEL.
I immediately before N and N immediately before S make the uninterrupted block INS. E immediately before L makes the block EL. Since L must be the sixth and final patch, E must be fifth.
The first four positions must therefore contain T and the intact block INS. Only two block orders are possible: T–INS or INS–T. The last note requires T before I, so only T–INS survives. Adding the fixed final EL gives TINSEL.
Every note can now be checked directly: I is second and N third; N is third and S fourth; E is fifth and L sixth; L is last; and T, in first position, precedes I.
The block argument proves uniqueness without consulting a dictionary. As a separate finite check, the six distinct patches have 720 possible orders. Exactly one satisfies all five notes. Treating the seam as a loop or weakening “immediately” to “somewhere” would admit different possibilities, which is why those conventions are explicitly fixed before the puzzle begins.
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