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Many words are balanced, but most are not. All of the following are examples of balanced words

GOLD LEMONS UNCOOKED BORDERLINE LILLIPUTIANS COUNTERBALANCE PREDETERMINATION

while none of the following are

GEMS ORANGE DIGESTED UNDENIABLE UNNOTICEABLE COUNTERMEASURE UNCOMPROMISINGLY

Only one the following is a balanced word; which one?

BACKGAMMON, CHECKERS, CHESS, CRIBBAGE, DOMINOES

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  • $\begingroup$ I found all but one of the bold words above are balanced. Surely I was wrong. :p $\endgroup$
    – LaBird
    Mar 27, 2015 at 11:30
  • $\begingroup$ @LaBird I just double checked and I don't think there's any error, perhaps you had a typo in transcription or something? $\endgroup$
    – KSab
    Mar 27, 2015 at 11:34
  • $\begingroup$ I didn't mean you made an error, actually I just believe my reasoning is far too simple: I just found all the bold words contain even number of letters except "CHESS". So I think it is unbalanced. :p $\endgroup$
    – LaBird
    Mar 27, 2015 at 11:38
  • $\begingroup$ @LaBird Ah, maybe to be more rigorous I should include a list of words that are not balanced :p $\endgroup$
    – KSab
    Mar 27, 2015 at 11:39

1 Answer 1

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Addition of even<->odd alphabets positions as they appear in aphanumeric order...

GOLD,7,15,12,4=>19<->19 balanced

LEMONS,12,5,13,15,14,19=>39<->39 balanced

UNCOOKED,21,14,3,15,15,11,5,4=>44<->44 balanced

BORDERLINE,2,15,18,4,5,18,12,9,14,5=>51<->51 balanced

LILLIPUTIANS,12,9,12,12,9,16,21,20,9,1,14,19=>77<->77 balanced

COUNTERBALANCE, ---->balanced

PREDETERMINATION, ---->balanced

so the answer is :

BACKGAMMON

to see how they balence:

BACKGAMMON,2,1,3,11,7,1,13,13,15,14 => 40 <-> 40 Balanced

CHECKERS,3,8,5,3,11,5,18,19 => 37<->35 NOT BALANCED

CRIBBAGE,3,18,9,2,2,1,7,5 => 21<->26 NOT BALANCED

DOMINOES,4,15,9,13,15,5,19 => 47<->31 not balanced

Used following ref :

1 2 3 4 5 6 7 8 9 10 11 12 13

a b c d e f g h i j k l m

z y x w v u t s r q p o n

26 25 24 23 22 21 20 19 18 17 16 15 14

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    $\begingroup$ What I was working toward but you beat me too it....good job. You might get some backlash for formatting. $\endgroup$
    – kaine
    Mar 27, 2015 at 11:58
  • $\begingroup$ @kaine i am new here.How can i put answer as that appears in yellow bar.I gave 4 spaces before my answer but it is looking grayed (i do it on stackoverflow for coding). $\endgroup$
    – user2408578
    Mar 27, 2015 at 12:01
  • $\begingroup$ The yellow bar is done by putting ">!" in front of the line. For some reason it seems to mess up if you do it for two lines in a row. That is about all I know on spoiler tags. Here I did it as a edit you can see how. $\endgroup$
    – kaine
    Mar 27, 2015 at 12:03
  • $\begingroup$ Correct! Another way of wording it is that the alternating sum of the letters equals zero: 7 - 15 +12 - 4= 0. I only used even length words too avoid situations where might have used ASCII encodings or something to calculate it (with even letters it works either way) $\endgroup$
    – KSab
    Mar 27, 2015 at 12:07

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