Case 32 · cipher · Medium · About 6–10 minutes
A postmaster uses two small operations to disguise short delivery instructions. He has written down his complete procedure, but left the wheel setting on yesterday’s test slip.
The sealed parcel must go to one destination. Recover the instruction without guessing what would be a sensible place to hide it.
Here is the ordinary alphabet:
ABCDEFGHIJKLMNOPQRSTUVWXYZ
To encrypt, move every letter forward by the same number of alphabet positions, wrapping Z back to A. The setting is a whole number from 1 through 9. Then reverse the letters inside each word. Leave the word order and spaces unchanged.
The test slip records an original word and its final encrypted form:
INK → NQL
The parcel’s encrypted instruction is:
QHSR HKW HXOE ARE
Find the setting, then recover the instruction. The test and the parcel use exactly the same procedure and setting. There are no missing letters, extra reversals, or changes to the spaces.
You can make a paper alphabet wheel if useful. Its appearance is optional; an ordinary written alphabet contains everything the method needs.
Hint 1 - reveal when you want a nudge
Undo the final operation first. Reverse NQL before comparing it with INK.
Hint 2 - reveal when you want a nudge
NQL reversed is LQN. I becomes L, N becomes Q, and K becomes N: each move is three places forward.
Reveal the solution and explanation
The setting is 3, and the instruction is OPEN THE BLUE BOX.
The calibration resolves the setting rather than leaving it to the plausibility of the final sentence. Reversing NQL gives LQN. Comparing corresponding letters with INK gives a shift of three in every position. Of the allowed settings 1–9, only 3 maps I to L; the other two letters independently confirm it.
Now reverse each encrypted word: QHSR becomes RSHQ, HKW becomes WKH, HXOE becomes EOXH, and ARE becomes ERA. Move every letter three places backward. The four results are OPEN, THE, BLUE, and BOX.
Notice that the words themselves never exchange positions. Reversing the entire line would undo an operation the postmaster never performed.
For a check in the original direction, shift OPEN forward three places to RSHQ, then reverse it to QHSR. Repeating that check for all four words recreates the complete printed ciphertext. A fixed shift is a one-to-one letter mapping and word reversal is reversible, so the calibrated procedure permits only one plaintext, whether or not a solver recognizes the sentence early.
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