## Task 21/62

![](https://cdn.mathpix.com/cropped/2024_06_06_1d2be4837fb839c2b31dg-046.jpg?height=223&width=1010&top_left_y=891&top_left_x=523)

In a keyless padlock, the bolt part with four identical and equally spaced teeth on one side is inserted into a sleeve with four identical rings that can rotate independently around the bolt axis (see figure). This is only possible in a specific position of the rings, as is the opening of the lock.

On the rings, six letters are engraved; four of them (one per ring) form the known key word when in the open position.

a) How many different key words are possible with this construction at each lock? A "key word" is any (even nonsensical) combination of four letters.

b) Compare the security of this lock with that of a similar lock that has six rings with four letters each.

c) How many different rings with six different letters from the 26 letters of the alphabet can the manufacturing company produce?

Rings are considered the same if they have the same letters (regardless of order) and the notch is under the same letter.

d) How many locks with different key words can be made from these rings?