Combination of lock with adjustable key and core

A combination of a lock and a key, comprising:

• a cylinder having a housing, multiple index rings and multiple cores, the housing having a passage defined axially therethrough, a slot laterally defined through a wall of the housing, at least one first post extending radially from a first end of the housing, at least one second post extending radially from a second end of the housing;
• the index rings located in the passage and each index ring having at least one column extending radially therefrom which extends through the slot and has a first mark, at least one cap restricting the index rings to the housing, each index ring having one of the cores received therein;
• a key having a handle, a shaft and multiple unlocking members, the handle connected to outer threads on one end of the shaft by a control member, each unlocking member having a mounting hole through which the shaft of the key extends, each unlocking member having a second mark and a top portion, and
• the index rings being removed and re-arranged via the slot by removing the cap, different combinations being created by matching the first marks of the index rings and the second marks of the unlocking members of the key.