# Odds of there being two solutions to a word puzzle [closed]

What are the odds of there being two solutions to, say, a cryptoquote? And is anyone aware of an example of such?

• Not sure what exactly you're asking for here. You'd need a very long list of everything you consider a "quote" (with very short ones) to give you a percentage. If it's just about a string of arbitrary words, we'd need to know the which word list shall be used (ie what counts as a word) Jul 6 at 13:42
• If there's two equally good solutions to a puzzle, it's a bad puzzle Jul 6 at 14:25
• Bobble, I'd agree in the case of most other types of puzzles, but in the case of a cryptoquote I would have to disagree. It would be fascinating! At least to me.
– JoeB
Jul 6 at 16:03

Here is a very simple example using rot13.com. I could have the cipher text of ozsl but that can be decrypted to what using rot8, alex using rot12, or jung (a common last name in my hometown) using rot21.

But note that the more complex the message and the more exclusive the hints are, the more likely there is a unique answer. For instance, with the example I gave above, you could create the following puzzle:

Cipher text is ozsl
It is what I call my best friend
You can find many of these in Germany

It doesn't have many constraints and has the two solutions I gave above (Alex is a common German first name and Jung is a common German last name). But if you add another constraint, it now has one valid answer.

Cipher text is ozsl
It is what I call my best friend
You can find many of these in Germany
There are at least two vowels

This is one of the reasons that people will add hints or revisions to their puzzles, because something wasn't clear enough or there was an alternate solution that they didn't think of.

• "what" is arguably also correct for the first riddle, considering "it is What i call my best friend..." :) Jul 6 at 21:44

It depends on the puzzle type, text length and also on the language, but apart from minor variations (like rare letters in proper nouns) and deliberately constructed "ciphertext collisions", the solution to a cryptoquote is almost certainly unique.

A cryptoquote is just a substitution cipher, so 28 letters is a sufficient amount of ciphertext that will allow decryption without any prior knowledge of the plaintext: at that length there's likely to be only one reasonable sentence that could have produced the ciphertext.

Since we know the plaintext is going to be a quote, the required text length will go down by several letters (because anything that doesn't look like a quote is ruled out), so as long as the quote has more than five words or so, the name of the quotee will almost certainly bring the ciphertext amount over the unique solution threshold.

If the quote is very long (say, over 50 letters), it becomes astronomically unlikely that there would be two grammatically correct sentences that would fit the ciphertext.