# Holiday puzzle: Anagrams modulo two

At today’s “Gathering 4 Gardner” social, Gordon Lessells presented his annual Christmas puzzle. The mechanism, which he just started playing with a couple of weeks ago, is “cancelling pairs of duplicate letters.” For example, when you cancel each pair of duplicate letters in the word LESSELLS, you throw out EE, LL, and SS and are left with LS. If you cancel each pair of duplicates in TENNESSEE, you’re left with simply T.

Gordon presented a series of puzzles constructed by taking a fixed set of elements (e.g. counties of Ireland, presidents of the U.S., atomic elements, famous mathematicians); pairing them up in a perfect matching; cancelling duplicate letters in each pair’s sum; and presenting the resulting anagrams for decoding. His name for the genre is “Restoration.”

The following puzzle pairs up all 56 populated U.S. states and territories in that way; your task is to decode each cancelled anagram into its two constituents. For example, the first entry below is MILK; that’s the sum of OHIO and OKLAHOMA (casting out the duplicate letters AAHHOOOO). The second entry is HABIT OF USE; that’s the sum of DISTRICT OF COLUMBIA and NORTHERN MARIANA ISLANDS (casting out AAAACCDDIIIILLMMNNOORRRRSSTT). The rest are left as puzzles for you to solve.

1. MILK = OHIO + OKLAHOMA
2. HABIT OF USE = DISTRICT OF COLUMBIA + NORTHERN MARIANA ISLANDS
3. CUTWORK = NEW YORK + ___
4. DINOS = ___ + ___
5. LICH = ___ + ___
6. IVANHOE = ___ + ___
7. OUR = ___ + ___
8. READILY = ___ + ___
9. BOLT = ___ + ___
10. HANDIWORK = ___ + ___
11. MANURE = ___ + ___
12. NEWPORT = ___ + ___
13. WACO = ___ + ___
14. HAZELS = ___ + ___
15. MINSTREL = ___ + ___
16. LIKE CATSUP = ___ + ___
17. SERB = ___ + ___
18. VULGAR SIKH = ___ + ___
19. TWIN CAMEOS = ___ + ___
20. KNIGHTS’ ROW = ___ + ___
21. SIMPLY ROT = ___ + ___
22. GLUM CHAOS = ___ + ___
23. FLED = ___ + ___
24. LARCH FUTON = ___ + ___
25. MORE JIGS = ___ + ___
26. OCH = ___ + ___
27. WETS = ___ + ___
28. RUNS = ___ + ___

The 51 states and territories that remain to fill in are: Alabama, Alaska, American Samoa, Arizona, Arkansas, California, Colorado, Connecticut, Delaware, Florida, Georgia, Guam, Hawaii, Idaho, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, Maine, Maryland, Massachusetts, Michigan, Minnesota, Mississippi, Missouri, Montana, Nebraska, Nevada, New Hampshire, New Jersey, New Mexico, North Carolina, North Dakota, Oregon, Pennsylvania, Puerto Rico, Rhode Island, South Carolina, South Dakota, Tennessee, Texas, Utah, Vermont, Virgin Islands, Virginia, Washington, West Virginia, Wisconsin, Wyoming.

Hints: The first three blanks’ answers are all red states, in a sense. Each pair of states in #5, #6, #19, #23 share a land border; #17’s border was historically significant. You might find #14, #25, and #27 easier to solve than the rest. And the answer to #28 may come as a surprise!

Posted 2023-12-24