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Two times n equals 2n-1 (Posted on 2012-09-25) Difficulty: 3 of 5
This is an extension of Two times three equals five.

Form words length of 2n-1 (n ≥ 3) such that, each (2n-1) letter word is the result of two n-letter words, the final letter of the first being the initial one of the second word. (It may be observed that, rip & pen → ripen is a valid example when n = 3.)

What is the largest value of n for which this is possible?

*** Proper nouns, acronyms, abbreviations, hyphens or spaces are not allowed.

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 2 of 2 |

My word list is a bit different from Dej Mar's. I found the highest n to be 9 using a different word from either of his.

DECLARE FUNCTION isWord! (w$)
CLS
OPEN "\words\words.txt" FOR INPUT AS #1
OPEN "2xnq2n-1.txt" FOR OUTPUT AS #3
DO
 LINE INPUT #1, w1$
 IF w1$ = LCASE$(w1$) AND LEN(w1$) MOD 2 = 1 THEN
   l2 = INT(LEN(w1$) / 2 + 1)
   IF isWord(LEFT$(w1$, l2)) AND isWord(RIGHT$(w1$, l2)) THEN
     l = LEN(w1$)
     IF l > 11 THEN
      PRINT USING "## & & &"; l; w1$; LEFT$(w1$, l2); RIGHT$(w1$, l2)
      PRINT #3, USING "## & & &"; l; w1$; LEFT$(w1$, l2); RIGHT$(w1$, l2)
     END IF
   END IF
 END IF
LOOP UNTIL EOF(1)
CLOSE

FUNCTION isWord (w$)
 n = LEN(w$)
 w1$ = SPACE$(n)
 OPEN "\words\words" + LTRIM$(STR$(n)) + ".txt" FOR BINARY AS #2
 l = LOF(2) / n
 low = 1: high = l
 DO
  mid = INT((low + high) / 2)
  GET #2, (mid - 1) * n + 1, w1$
  IF w1$ = w$ THEN isWord = 1: CLOSE 2: EXIT FUNCTION
  IF w1$ < w$ THEN low = mid + 1:  ELSE high = mid - 1
 LOOP UNTIL low > high
 isWord = 0
 CLOSE 2
END FUNCTION

produces a file which, when sorted, contains:

2n-1 words
17   architectonically architect tonically
15   countershadings counters shadings
15   counterstaining counters staining
15   counterstepping counters stepping
15   counterstrategy counters strategy
15   dessertspoonful desserts spoonful
15   electronegative electron negative
15   electrosurgical electros surgical
15   featherstitched feathers stitched
15   featherstitches feathers stitches
15   snippersnappers snippers snappers
15   thunderstricken thunders stricken
15   thunderstriking thunders striking
15   troubleshooters troubles shooters
15   troubleshooting troubles shooting
15   whippersnappers whippers snappers
13   bittersweetly bitters sweetly
13   breaststroker breasts stroker
13   breaststrokes breasts strokes
13   candlesnuffer candles snuffer
13   chlorinations chlorin nations
13   chromospheres chromos spheres
13   chromospheric chromos spheric
13   coagulability coagula ability
13   condemnations condemn nations
13   conductresses conduct tresses
13   consignations consign nations
13   consumeristic consume eristic
13   doublespeaker doubles speaker
13   electrologies electro ologies
13   electrologist electro ologist
13   enchantresses enchant tresses
13   fellowshipped fellows shipped
13   fluorinations fluorin nations
13   germinability germina ability
13   halogenations halogen nations
13   happenstances happens stances
13   impregnations impregn nations
13   inheritresses inherit tresses
13   letterspacing letters spacing
13   mantelshelves mantels shelves
13   mastersingers masters singers
13   masterstrokes masters strokes
13   mineralogical mineral logical
13   monofilaments monofil laments
13   ossifications ossific cations
13   pacifications pacific cations
13   preformatting preform matting
13   pretermission preterm mission
13   protectresses protect tresses
13   pseudoscience pseudos science
13   psychosomatic psychos somatic
13   psychosurgeon psychos surgeon
13   psychosurgery psychos surgery
13   replicability replica ability
13   scatterations scatter rations
13   stigmasterols stigmas sterols
13   stipendiaries stipend diaries
13   thermosetting thermos setting
13   thermospheres thermos spheres
13   thermospheric thermos spheric
13   thermostating thermos stating
13   vivifications vivific cations
13   volcanologies volcano ologies
13   volcanologist volcano ologist
13   wafflestomper waffles stomper

showing a largest value of n as 9, as the longest word is 17 = 2n-1.


  Posted by Charlie on 2012-09-25 14:44:14
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