# Winning Conditions (solution)

## by Josh Ain and Kai Huang with additional code by C. Scott Ananian and Andrew Lin

The idea is that by playing around with the app, you should discover more and more about how the game works. The most obvious thing is to figure out the 10 rules. They are:

• Rule 1/10: Your guess must not be a repeat of a previous guess.
• Rule 2/10: Your guess must be a valid word in the SOWPODS list.
• Rule 3/10: Your guess must be at least 5 letters in length.
• Rule 4/10: Your guess must have at least 3 different letters.
• Rule 5/10: Your guess must not have any anagrams in the SOWPODS list.
• Rule 6/10: Your guess must only contain letters found in the word “ANSWER”.
• Rule 7/10: Your guess must only contain letters found in the word “WORDPLAY”.
• Rule 8/10: Your guess must produce an anagram of itself (not necessarily a valid word) when rot13 is applied.
• Rule 9/10: Your guess must have the property that moving its first letter to the end creates a valid word in the SOWPODS list.
• Rule 10/10: Your guess must contain a letter that appears 4 times consecutively.

It’s clear that not all of these rules can be satisfied by one guess. For example, no word in the SOWPODS list contains a letter that appears 4 times consecutively. The next thing to realize is that not all rules are in effect for each guess. By experimentation, you’ll discover that the same subset of rules are always in effect for each guess number. Furthermore, after figuring out the rules in effect for the first few guess numbers (say guess numbers 1-6), you may be able to conjecture some patterns. The rule enforcement patterns are as follows:

• Rules 1 and 2 are always in effect.
• Rules 3 and 4 are in effect for even and non-even (odd) numbers, respectively.
• Rules 5 and 6 are in effect for prime and non-prime numbers, respectively.
• Rules 7 and 8 are in effect for square and non-square numbers, respectively.
• Rules 9 and 10 are in effect for fibonacci and non-fibonacci numbers, respectively.

Given the either-or nature of the paired rules, only one combination of rules is satisfiable. Specifically, all the rules in effect are satisfiable only when the guess number is odd, non-prime, non-square, and fibonacci. The first such guess number is 21. The one word that can satisfy all of the rules 1, 2, 4, 6, 8, and 9 is NEAR.

And it’s a good thing that guess number 21 is satisfiable. Due to the fact that there are only 10 rules and you can only break each rule twice, by the time you get to guess number 21, you’ve exhausted all your wrong guesses. Either you win the game on guess number 21, or you lose due to breaking some rule for the third time.

Thus, in order to win the game on guess number 21, you must plan out the game such that you break each rule exactly twice in the first 20 guesses. There are many ways to do this. Here’s one example.

Guess number Guess Rule broken Guess number Guess Rule broken Guess number Guess Rule broken
`  NEAR is correct. Another way of saying 'NEAR' is 'SO CLOSE'.`