Case 34 · cipher · Medium · About 7–10 minutes
A clockmaker dislikes a cipher wheel that stays still. Her encrypted note advances the alphabet setting after every letter, and the mechanism remembers how many letters have already passed.
The note identifies a drawer. Its full operating instructions survived, so the challenge is careful reversal rather than guessing a secret rule.
Use the alphabet ABCDEFGHIJKLMNOPQRSTUVWXYZ, with wraparound after Z.
The clockmaker first removes all spaces from an instruction. She encrypts its first letter by shifting it forward one place, the second by two places, the third by three places, and so on. Letter number fourteen is shifted fourteen places. No position resets at a word boundary.
Her complete ciphertext is:
UCNIYNPZMNCMJSG
There are fifteen letters. Recover them, then restore the spaces using the supplied word lengths: 4, 5, 6.
A miniature example of the method is CAT → DCW: C moves one place to D, A moves two places to C, and T moves three places to W. This example is separate from the drawer instruction; do not count its letters when setting the shift.
What instruction did the clockmaker write? No extra substitution, reversed reading order, or interpretation of the picture is involved.
Hint 1 - reveal when you want a nudge
Number the ciphertext letters 1 through 15. Decryption moves backward by the corresponding number, not forward again.
Hint 2 - reveal when you want a nudge
The first four calculations are U−1=T, C−2=A, N−3=K, and I−4=E. Keep increasing the shift after this first word.
Reveal the solution and explanation
The instruction is TAKE THIRD DRAWER.
Subtracting the position from each encrypted letter yields TAKETHIRDDRAWER. The supplied lengths divide this into TAKE, THIRD, and DRAWER. The spaces are fixed by the instructions rather than supplied by an assumption about sensible English.
Here are useful checkpoints. Position 5 is Y; moving backward five places gives T, the beginning of THIRD. Position 9 is M; moving backward nine places gives D, its final letter. Position 10 is N; moving backward ten places gives D, the beginning of DRAWER. The final G moves backward fifteen places, wrapping around the alphabet, to R.
A common near-solution comes from restarting the count at the second word. That would use a shift of one at position 5, contradicting the rule that spaces were removed before encryption.
Each position has one specified shift, and shifting an alphabet is reversible. Consequently every ciphertext character has exactly one predecessor. As a separate check, encrypting all fifteen recovered characters with shifts 1–15 reproduces UCNIYNPZMNCMJSG character for character. There is no competing key to select by taste or context.
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