There is a safe containing millions of dollars – unfortunately the combination is written on only one card, and that card has been accidentally locked inside the safe! If the wrong combination is used, the lock will jam and the only way to open the safe would be to blow it up, destroying the contents.

A combination is a string of digits from 0 through 9. It can be any length and contain any number of digits occurring any number of times; 90915 is a combination; so is 2133127; so is 5. Certain combinations will open the lock, certain combinations will jam the lock, and the remaining combinations will have no effect whatever (these last are called neutral).

The small letters x and y will represent arbitrary combinations, and by xy is meant the combination x followed by the combination y; for example, if x is 213 and y is 3812, then xy is 2133812. By the reverse of a combination is meant the combination written backwards; for example, the reverse of 3812 is 2183. By the repeat xx of a combination x is meant the combination followed by itself; for example, the repeat of 3182 is 31823182.

Now, some of the combinations are related to other combinations. There are five properties of this relation:

There is no way to prove, just from the evidence given, whether any arbitrary "invalid" combination is "jamming," or neutral, and it is concievable that there are some series of "valid" combinations that can't be proved "valid." But there are ways to prove certain combinations "valid."

All of this comes from rule E (see my earlier post). The next step is to de-construct the first four rules to build a combination from scratch that will generate the series needed to prove it is "valid"

Posted by TomM on 2002-07-16 17:39:37