# Don't Let Me Down

### by Mark Halpin and Dave Shukan

There is only one way to fill in the hangman words using 26 different guesses (at least according to words in Webster's Collegiate 11th ed., Webster's Third New International Unabridged, and Onelook.com):

1. Only place for X to go is 12 = LAXLY = LX (even true for words taking 3 letters)
2. With L gone, 8 = UNIQUE = IQ
3. With I gone, 1 = SUMMON = ON
4. With N gone, 2 = ROTGUT = RT
5. With L and R and Q gone, 11 = KVASS = KV
6. With 13 not AL, only place for A is 4 = CRASES, ERASES, GRASPS, or PRASES
7. With T gone, only place for Z is 3 = BOOZY, DOOZY, or WOOZY
8. With R and 3 and 12 gone, J can only go in 7 = CJ or JU
9. With R and 2 gone, 9 = DIDST or MIDST
10. With D in 9 and K and 3 and 4 and 12 gone, only place left for M is 9 = MIDST = DM
11. With 3, 9, and 12 gone, no word can be filled by a single guess, and thus all words must be filled by exactly 2 guesses (a 3 would need a 1 somewhere), and thus 4 = ERASES = AE
12. With K and R gone, 7 = BYWAYS = SY
13. With Y gone, 13 = SHOGUN = HU
14. With U gone, 7 = JACK = CJ
15. By inspection, the remaining BFGPWZ can only work as 3 = WOOZY, 5 = BURGER = BG, 10 = SPOOF = FP

Using A = 1, B = 2, etc, these 13 bigrams yield 13 different differences (taking smaller from larger), ranging from 1 to 13. Arranging the games in this order (instead of the given order which was alphabetical by correctly guessed letters) yields the grid below.

WordBigramIncorrect guesses
SUMMONNO (1)HERCA
ROTGUTRT (2)ELAKD
WOOZYWZ (3)GLNET
ERASESAE (4)UNKJO
BURGERBG (5)IHAOJ
BYWAYSSY (6)TUHDO
JACKCJ (7)ESOLI
UNIQUEIQ (8)ASRDH
MIDSTDM (9)UENBA
SPOOFFP (10)RITEL
KVASSKV (11)PNFTE
LAXLYLX (12)OIRHS
SHOGUNHU (13)WFIEC

Examining the 5x13 grid of incorrect letters vertically downward (and continuing at the top of the next column, when necessary) reveals the names of people executed by hanging (GUITEAU, POWELL, HUSSEIN, FRANK, HORN, FRICK, JODL, BETHEA, TOJO, HALE -- several of these should be recognizable without research, and lists on Wikipedia and elsewhere contain them all in one place). The unused letters (2 at the beginning, 2 at the end, and one between each pair) spell the answer HERNIATED DISC, one of the less troublesome ailments that might be caused by a hanging.

Upon completing this puzzle, the following set of cards is revealed on the round page: