# CISRA Puzzle Competition 2011 - Solutions

## 4D. Puzzle Competition Reminder

The text shows an e-mail chain that "inadvertently" gives away details of a puzzle. This is the actual puzzle and we have to work out what it is from the information provided or hinted at. Working from the oldest e-mail first, we tease out some information:

• Some words are anagrammed and placed in a grid; two non-adjacent letters in each word are marked, in different colours. The indicated letters are then anagrammed to produce two seven-letter words. So there are seven words to find.
• Each "word" is first given with its letters sorted into alphabetical order. Each anagrams to a state.
• The two seven-letter words formed are "WAXHEAD" and "ZOMBIES", so one letter from each of these must be part of the set of seven initial words. The states are confirmed to be US states, and California is not one of them.
• The seven states are geographically contiguous. All of them share a letter between state and capital city names. Precisely one of the four-letter states is involved.
• The fourth letter of each state provides some sort of "secret hint" to solving the puzzle.

So... we want seven US states, geographically contiguous, which can form WAXHEAD ZOMBIES by suitable choices of letters, and some other conditions which we will factor in at appropriate points. Some initial observations:

• The Z can only come from Arizona.
• The B can only come from Nebraska or Alabama.
• The X can only come from New Mexico or Texas.
• Utah has no letters in common with ZOMBIES, so is ruled out.
• Missouri, Mississippi, and Illinois have no letters in common with WAXHEAD, so are ruled out.
• Kentucky only has the E in common with either word, but needs two different letters, so is ruled out.

With those ruled out, it is not possible to get from Ohio to Arizona in seven states. Thus Ohio is also ruled out. Since Utah and Ohio are eliminated, and precisely two four-letter states are excluded, Iowa (which also has four letters) must be in the set.

If Alabama is in the set, then it must connect through Tennessee and Arkansas. But then the set contains Alabama, Arkansas, and Arizona, all of which only have an A in common with WAXHEAD. Since WAXHEAD only has two A's, this is not possible. Thus Alabama is not in the set, and Nebraska must be in order to supply the B.

Since Nebraska gives B for ZOMBIES, the WAXHEAD marked letter in it cannot be E (as this is adjacent to the B). It must therefore be A. Arizona must supply A and Z. Consequently, both of the A's in WAXHEAD are allocated and Iowa must provide W to WAXHEAD, and thence I to ZOMBIES (by non-adjacency).

With AAW/ZIB allocated already, we can rule out some more states:

• Kansas, Arkansas, Wisconsin, Wyoming, and Montana have no letters in common with XHED, and so are ruled out.

At this point New Mexico and Colorado are definitely required in order to connect Arizona to Nebraska and Iowa, which are mostly surrounded by excluded states. Colorado must supply D and O. Nevada is now ruled out of consideration.

The condition that the state capitals must share a letter with the state rules out South Dakota (capital city: Pierre). In fact, this is the only state ruled out by that condition.

An H and S are still required from the remaining two states (and definitely from different states now that South Dakota is ruled out). The S can come from Minnesota or Texas; however, in Minnesota, the E would also have to be used as part of WAXHEAD (since the A's are used up). Since the S and E are adjacent, this is not allowed and the S must come from Texas. The only adjacent H remaining is that of Oklahoma. The complete list of states and marked letters is:

 Arizona A Z Colorado D O Oklahoma H M Nebraska A B Iowa W I New Mexico {EX} E Texas {EX} S

We now have the seven states - a quick check shows that we can, indeed, form WAXHEAD and ZOMBIES from them with non-adjacent letters. What next?

We haven't used the information about the fourth letters spelling out a "secret hint". Taking those fourth letters we get ZMAORAA, which does not seem to make anything useful no matter how we arrange it. But remember that the states were originally given as anagrams with the letters individually sorted in alphabetical order.

 TEXAS AESTX T IOWA AIOW W NEW MEXICO CEEIMNOWX I ARIZONA AAINORZ N OKLAHOMA AAHKLMOO K COLORADO ACDLOOOR L NEBRASKA AABEKNRS E

In that form, the fourth letters (alphabetically) are NLKEWIT, which anagram to the "secret hint": TWINKLE. This, being the most significant piece of unknown information about the "leaked" puzzle, is the solution to the actual puzzle. (This may seem appropriate when considering how the states are represented on the US flag - as stars.)

Puzzle design notes:

Although it's not necessary to solve the puzzle, there is enough information given to work out the configuration of the letter grid mentioned. We're told the column containing the "secret hint" is made up of the fourth letters, so arranging the states to spell out TWINKLE down a column allows you to disambiguate the EX between Texas and New Mexico by the non-adjacency criterion, applied vertically.

The only thing this leaves unexplained is how the word TWINKLE is a hint pointing at the "solution" of WAXHEAD ZOMBIES. We leave this as an exercise for the puzzle solver. (Hint: it involves familiarity with Californian science fiction surfer culture...)