Select the word which cannot be formed using the letters of the given word:…

Concept

A word can be formed from a source word only if, for every letter, the number of times it is needed does not exceed the number of times it appears in the source. This is a letter-frequency (multiset) test: counting how many of each letter are available, not merely whether a letter exists at all. A repeated letter in the target demands an equal number of copies in the source.

Application

Source word 'Nightwalker' has the letters N, I, G, H, T, W, A, L, K, E, R — 11 distinct letters, each appearing exactly once. So any target needing a letter twice will fail, since no letter is available more than once.

1. Talker needs T, A, L, K, E, R — each needed once and each available once. Formable.

2. Tailer needs T, A, I, L, E, R — each needed once and each available once. Formable.

3. Waller needs W, A, L, L, E, R — this asks for the letter L twice, but only one L is available. Not formable.

4. Winer needs W, I, N, E, R — each needed once and each available once (note N is the first letter of Nightwalker). Formable.

Cross-check

Only one target repeats a letter that the source supplies just once: Waller (two L's). The other three use distinct letters that are all present, so they are buildable. Hence the word that cannot be formed is Waller.