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4-Letter Words (Posted on 2009-08-09) Difficulty: 3 of 5
I've just joined the YMCA and bought a lock to put on a locker. I bought one where you can choose your own combination. It has four rings surrounding the cylinder: the four inner rings have four dots that, when lined up, indicate the lock is in the open position. The lock came with eight outer rings from which the user can choose four to cover the inner rings, choosing one of ten characters on each ring to be over the red dot on the inner ring that it covers, thereby forming the combination.

I chose to use the four numeric rings (digits 0 - 9), but an interesting puzzle can be made from the rings having alphabetic characters.

The first ring has the letters A - J; call this type 1 ring. The second and third rings each have the letters K - T; call these type 2 rings. The fourth ring has letters U - Z and four special symbols. We'll ignore the ampersand, hyphen, blank and exclamation mark, but you might wish to explore such things as L&ER, for "lander" on your own.

Although foolish from a security standpoint, the use of a real word has mnemonic value. The foolishness is especially true as the specific hard-and-fast choice of the sequence of types, which can't be altered by someone merely opening the lock, limits the possible words that might be the key. For example if the sequence of types fixed onto the rings was 3221, few common words would be possible, like ULNA, VOLE, VOTE, WOKE, WOLF, WOMB, WOOD, WOOF, WORD, WORE, YOKE, YORE and ZONE. A potential thief could go through these quickly.

So categorize, by the sequence of type of ring, the possible 4-letter words that might be chosen as the unlocking key, given that there are one each of types 1 and 3, and two of type 2.

There are no tricks like treating W and M interchangeably, as, first of all, one is not really the upside-down of the other, and second, the one being used would be given away by the fact that all the other letters would be upside-down also.

See The Solution Submitted by Charlie    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: Categories? | Comment 3 of 5 |
(In reply to Categories? by Dej Mar)

That's what I had in mind, yes. However there are 12 categories (4!/2!), including 2312 and 2321.
  Posted by Charlie on 2009-08-10 11:25:34

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