Brain-Teaser 475

From The Sunday Times, 5th July 1970 [link]

The lockers in one section of the new club-house are numbered 1 to 12 consecutively. Last Saturday, Pitcher arrived without his key. He was surprised to find that his locker could be opened by the key to Putter’s locker which is next to his.

Pitcher at once saw Wedge, the secretary, and Bunker, the captain. From them he learned that there are only 3 different key patterns for the 12 lockers (patterns A, B and C) and that the total of the numbers on the 4 A lockers is the same as the corresponding total for the 4 B lockers, which is the same as that for the 4 C lockers.

Wedge also told Pitcher that no two lockers with pattern A keys are adjoining. He added that his own key is of the same pattern as Wood’s and that the total of the numbers on Wood’s and Wedge’s lockers is 16. He further mentioned that of the 3 lockers, other than the captain’s own locker, which can be opened by the captain’s key, the nearest to the captain’s locker is further from the captain’s locker than are 5 (but not more) lockers which cannot be opened by the captain’s key.

By this time, Pitcher was making for the wall but if the number on Putter’s locker is higher than the number on Wedge’s locker — what is the number on Bunker’s locker?