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


while none of the following are


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


  • $\begingroup$ I found all but one of the bold words above are balanced. Surely I was wrong. :p $\endgroup$ – LaBird Mar 27 '15 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 '15 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 '15 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 '15 at 11:39

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


so the answer is :


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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  • 3
    $\begingroup$ What I was working toward but you beat me too it....good job. You might get some backlash for formatting. $\endgroup$ – kaine Mar 27 '15 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 '15 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 '15 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 '15 at 12:07

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