In a certain code, CLOCK is written as KCOLC. How would STEPS be written in…
2009
In a certain code, CLOCK is written as KCOLC. How would STEPS be written in that code?
Answer: C. SPETS — ConceptIn a letter-coding question the code word is built from the original word by one fixed positional rule, so the first job is to line the two words up…
- A.
SPEST
- B.
SPSET
- C.
SPETS
- D.
SEPTS
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept
In a letter-coding question the code word is built from the original word by one fixed positional rule, so the first job is to line the two words up letter by letter and record where each letter has moved. The most common such rule is complete reversal: in an n-letter word the letter standing at position i is written at position n + 1 - i, which is the same as writing the word backwards.
Application
Line up the given pair position by position.
Position | Letter in CLOCK | Letter in KCOLC |
|---|---|---|
1 | C | K |
2 | L | C |
3 | O | O |
4 | C | L |
5 | K | C |
Every letter travels from position i to position 6 - i: 1 swaps with 5, 2 swaps with 4, and the middle letter at position 3 stays where it is. So the rule of this code is simply to write the word backwards.
Write STEPS with its positions: S at 1, T at 2, E at 3, P at 4, S at 5.
Apply the mapping i to 6 - i: the S from position 1 moves to position 5, T from 2 moves to 4, E from 3 stays at 3, P from 4 moves to 2, and the S from position 5 moves to position 1.
Read the code off from position 1 to position 5: S, P, E, T, S, which spells SPETS.
Cross-check
Reversing SPETS gives back S, T, E, P, S, that is STEPS, so the rule works in both directions. Reversing each of the other arrangements does not return the original word:
SPEST reversed is TSEPS.
SPSET reversed is TESPS.
SEPTS reversed is STPES.
This is why the letters of a reversal code must be tracked one position at a time; arrangements that merely look scrambled in a similar way do not follow the same mapping.