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 Numbered Letters II (Posted on 2011-05-09)
Consider the values of the individual letters in Numbered Letters in their original order.

What are the English words that have a total letter value of exactly 100 when you add up all of the letters, whenever:

(I) Each of the letters in the odd positions have the same values as in the original system, but the letters in the even positions are assigned the values in reverse order (a=1, b=26, c=3, d=24, e=5, f=22, ..., y=25, z=2)?

(II) Each of the the letters in the even positions have the same values as in the original system, but the letters in the odd positions are assigned the values in reverse order(a=25, b=2, c=23, d=4, e=21, f=6, ..., y=1, z=26)?

 No Solution Yet Submitted by K Sengupta No Rating

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 Just for kicks Comment 4 of 4 |

I also added a check to see if any words had a value of 100 in more than one of the three schemes (the two from this problem and the original):

`my @results0;my @results1;my @results2;my @results3;my @results4;my @results5;open WORDLIST, "<words.dat" or die \$!;while(<WORDLIST>){	chomp \$_;	@word = split(//, \$_);	my @totals = (0,0,0);	foreach (@word)	{		my \$v = ord(\$_)-96;		\$totals[0] += \$v;		\$totals[1] += \$v%2?\$v:28-\$v;		\$totals[2] += \$v%2?26-\$v:\$v;	}	if (\$totals[0] == 100) { push @results0, join '', @word; }	if (\$totals[1] == 100) { push @results1, join '', @word; }	if (\$totals[2] == 100) { push @results2, join '', @word; }	if (\$totals[1] == 100 && \$totals[2] == 100) { push @results3, join '', @word; }	if (\$totals[0] == 100 && \$totals[1] == 100) { push @results4, join '', @word; }	if (\$totals[0] == 100 && \$totals[2] == 100) { push @results5, join '', @word; }}close (WORDLIST);print \$#results0+1, " for original:\n@results0\n";print \$#results1+1, " for part 1:\n@results1\n";print \$#results2+1, " for part 2:\n@results2\n";print \$#results3+1, " for parts 1 and 2:\n@results3\n";print \$#results4+1, " for original and part 1:\n@results4\n";print \$#results5+1, " for original and part 2:\n@results5\n";`

1297 for original:

1379 for part 1:

945 for part 2:

0 for parts 1 and 2:

117 for original and part 1:

abatements airdrops anginous appointed baguettes bedazzles botanist boycott carboxyl caryatids catechisms chastening consigns coonskin cousins coyness crudity curlily danewort delivery derogating dilatants driveling droopier elephants enclasping equalized estopped explodes farrows ferrums ferryman filtering fleawort footpaces forewarn glimpses gooneys grandaunt guarantied heelpost hospital hotness impaneling inferring infringer inkiness ioniums jostles jurassic lavenders liberator lumpens matchmaking mattedly minuses misdirect missus moderates molecular morphemic moussaka mullers mythos panderers pathless pesthole pharisees plastered plenums plummy plunging poorish portland postpaid preachings preordain procured producer radarscope refinery regimented resolved restocked scannings schematics scotchmen semaphore session shakeout sharpens shattered shovels sinewing slumps splining squaws stalemated standers steadiers striding teardown telephone therefore thickening threatened tidemarks toroids torqued towards trounced trudging typefaces unmown untidier whooper woeness

50 for original and part 2:

adulthood asbestos boskiest chutist coplots crusados decorous disjoint disjunct emptily fishnets housemen hurrayed hypoxic ingroup jillions merrily perturb plummet pounding pouring problems progeny putter pyrogen reissued residues sennits sheeneys shivers shrewder shrives snipers snivels soughing swashing theists tipless tuneably turtled unbroken underlay unrobing vacuums violins washings wednesday whisking windfalls wizards

Edited on May 10, 2011, 12:03 am
 Posted by DJ on 2011-05-09 23:58:41

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