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Forward and Backward Word Values (Posted on 2017-02-07) Difficulty: 3 of 5
Assign a value to each letter of the alphabet using the trivial forward assignment: A=1, B=2, ..., Z=26. Let the value of a word be the sum of its letters. For example the value of 'example' would be 5+24+1+13+16+12+5 = 76.

In contrast, assign the values backwards: A=26, B=25, ..., Z=1. Then 'example' would have a value of 22+3+26+14+11+15+22 = 113.

Most words will have different forward and backward values. One exception is the word 'by': it has a value of 27 both forward and backward. Can you find longer words whose forward and backward values are the same?

No Solution Yet Submitted by Brian Smith    
Rating: 4.5000 (2 votes)

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Solution computer solution (spoiler) | Comment 1 of 5
I guess these words are somewhat UNCOMMON (see below; length 8; value 108). Proper names have been included; just ignore them if you don't like them; they come before the uncapitalized words for a given length.

Each line has the number of letters, the word and the value (same in both systems).

  4 Brum 54
  4 Copt 54
  4 Eton 54
  4 Frey 54
  4 Inez 54
  4 Kurd 54
  4 Lely 54
  4 Mayo 54
  4 Musa 54
  4 Pavo 54
  4 Shri 54
  4 Slav 54
  4 Stan 54
  4 Zola 54
  4 tans 54
  4 taro 54
  4 taxi 54
  4 temp 54
  4 tipi 54
  4 tone 54
  4 tora 54
  4 trek 54
  4 trig 54
  4 undo 54
  4 vier 54
  4 viva 54
  4 vole 54
  4 weft 54
  4 whin 54
  4 woke 54
  4 wold 54
  4 yell 54
  4 yock 54
  4 yuga 54
  4 zebu 54
  4 zeds 54
  4 zein 54
  6 Bombyx 81
  6 Boulez 81
  6 Bumbry 81
  6 Conway 81
  6 Cripps 81
  6 Crusoe 81
  6 Dorset 81
  6 Ernest 81
  6 Florey 81
  6 Gullit 81
  6 Hudson 81
  6 Jewess 81
  6 Lottie 81
  6 Louise 81
  6 Lozere 81
  6 Moskva 81
  6 Muftat 81
  6 Nazify 81
  6 Nowell 81
  6 Orissa 81
  6 Phuket 81
  6 Podunk 81
  6 Pythic 81
  6 Quayle 81
  6 Ramsey 81
  6 Rienzi 81
  6 Rodney 81
  6 Samson 81
  6 Sartre 81
  6 Scarus 81
  6 Shiraz 81
  6 Sterne 81
  6 Thetis 81
  6 Torahs 81
  6 Torbay 81
  6 Tupian 81
  6 Veneto 81
  6 Vivien 81
  6 Wesker 81
  6 Wirral 81
  6 Xhosan 81
  6 Xmases 81
  6 Yorick 81
  6 sunder 81
  6 superb 81
  6 supped 81
  6 talons 81
  6 tarres 81
  6 tauten 81
  6 tennis 81
  6 tenser 81
  6 ternes 81
  6 terras 81
  6 tetchy 81
  6 theist 81
  6 thinks 81
  6 thrift 81
  6 tithes 81
  6 titmen 81
  6 tmeses 81
  6 toilet 81
  6 tolans 81
  6 toluid 81
  6 tonier 81
  6 toping 81
  6 torahs 81
  6 toroid 81
  6 toward 81
  6 tracts 81
  6 trains 81
  6 treens 81
  6 tropic 81
  6 tubule 81
  6 undraw 81
  6 uneven 81
  6 unlink 81
  6 unshod 81
  6 upases 81
  6 uprate 81
  6 uptear 81
  6 vacuum 81
  6 valves 81
  6 vermin 81
  6 vexing 81
  6 vibist 81
  6 violin 81
  6 vitric 81
  6 vulgar 81
  6 wahoos 81
  6 wanter 81
  6 warper 81
  6 wattle 81
  6 weekly 81
  6 wherve 81
  6 willet 81
  6 wising 81
  6 witted 81
  6 wizard 81
  6 wonted 81
  6 yapper 81
  6 yarner 81
  6 yclept 81
  6 yelper 81
  6 yoking 81
  6 yonder 81
  6 zibets 81
  6 zonate 81
  8 Apocynum 108
  8 Chrysler 108
  8 Guinness 108
  8 Gurmukhi 108
  8 Jahvists 108
  8 Jehovist 108
  8 Paterson 108
  8 Pullmans 108
  8 Realtors 108
  8 Scotsmen 108
  8 Serevent 108
  8 Smolensk 108
  8 Solihull 108
  8 Spartans 108
  8 Stirling 108
  8 Teletype 108
  8 Tylopoda 108
  8 sulphids 108
  8 summital 108
  8 surmised 108
  8 swampish 108
  8 swearers 108
  8 sweetish 108
  8 swingles 108
  8 swishing 108
  8 swooshed 108
  8 symbiote 108
  8 tantalus 108
  8 tarriers 108
  8 tepidity 108
  8 terawatt 108
  8 terrines 108
  8 thallous 108
  8 thinness 108
  8 thionins 108
  8 thirties 108
  8 thumping 108
  8 tightest 108
  8 tinklers 108
  8 toilsome 108
  8 tomatoes 108
  8 tonsilar 108
  8 toothing 108
  8 totalize 108
  8 traverse 108
  8 tribunes 108
  8 trimeter 108
  8 trisemes 108
  8 troilite 108
  8 truckler 108
  8 trudgens 108
  8 turbines 108
  8 tusklike 108
  8 twilight 108
  8 typifier 108
  8 tzarinas 108
  8 unbloody 108
  8 unbought 108
  8 uncloses 108
  8 uncomely 108
  8 uncommon 108
  8 unitized 108
  8 unliving 108
  8 unornate 108
  8 unreally 108
  8 unrhymed 108
  8 unserved 108
  8 unsolder 108
  8 unstacks 108
  8 untested 108
  8 ununited 108
  8 unversed 108
  8 unvoices 108
  8 unwinder 108
  8 upraises 108
  8 upstages 108
  8 utilidor 108
  8 valorize 108
  8 vaporish 108
  8 vaultier 108
  8 vaunting 108
  8 veinulet 108
  8 veluring 108
  8 venality 108
  8 vibrions 108
  8 viewings 108
  8 vinasses 108
  8 wardenry 108
  8 wareroom 108
  8 wariness 108
  8 wartimes 108
  8 whitefly 108
  8 whopping 108
  8 wingless 108
  8 winnocks 108
  8 wintling 108
  8 woodruff 108
  8 woodsier 108
  8 woodsmen 108
  8 writhing 108
  8 yakitori 108
  8 yeshivas 108
  8 zygomata 108
 10 Artaxerxes 135
 10 Bourbonist 135
 10 Chatsworth 135
 10 Chironomus 135
 10 Christmasy 135
 10 Herrnhuter 135
 10 Kenilworth 135
 10 Listerises 135
 10 Mongolizes 135
 10 Mousterian 135
 10 Osteolepis 135
 10 Poohsticks 135
 10 Pretorians 135
 10 Proserpine 135
 10 Shropshire 135
 10 Slavonises 135
 10 Socratizes 135
 10 Stephenson 135
 10 Waterhouse 135
 10 superlight 135
 10 supersales 135
 10 surrealism 135
 10 swallowing 135
 10 sweepingly 135
 10 switcheroo 135
 10 sybaritism 135
 10 syllabuses 135
 10 sympathies 135
 10 sympathise 135
 10 taxonomies 135
 10 teetotally 135
 10 telephotos 135
 10 tenotomies 135
 10 tentatives 135
 10 therapists 135
 10 thorougher 135
 10 throatiest 135
 10 tincturing 135
 10 tormenting 135
 10 tortricids 135
 10 townscapes 135
 10 trajectory 135
 10 tranquiler 135
 10 transfixes 135
 10 transmuted 135
 10 transplant 135
 10 traumatism 135
 10 traversals 135
 10 treasuries 135
 10 treatments 135
 10 trignesses 135
 10 triphthong 135
 10 triumphing 135
 10 troubadour 135
 10 trowelling 135
 10 truncation 135
 10 undercount 135
 10 underplays 135
 10 underslung 135
 10 understood 135
 10 undertones 135
 10 unicyclist 135
 10 unluckiest 135
 10 unresolved 135
 10 upsweeping 135
 10 urochromes 135
 10 vanquishes 135
 10 vasculitis 135
 10 victimizes 135
 10 viraginous 135
 10 vitrioling 135
 10 wastewater 135
 10 wellspring 135
 10 westerlies 135
 10 whipstitch 135
 10 whizzbangs 135
 10 widowhoods 135
 10 yellowlegs 135
 10 zookeepers 135
 12 Hollywoodise 162
 12 Mariolatrous 162
 12 Montessorian 162
 12 Thysanoptera 162
 12 superbnesses 162
 12 swampinesses 162
 12 sycophantism 162
 12 syncretising 162
 12 telephonists 162
 12 tensiometers 162
 12 thymectomize 162
 12 tracheostomy 162
 12 translations 162
 12 trapshooting 162
 12 tropospheric 162
 12 tuberosities 162
 12 unauthorized 162
 12 underwriting 162
 12 unevennesses 162
 12 ungratefully 162
 12 universalism 162
 12 unobstructed 162
 12 unsterilized 162
 12 vainglorious 162
 12 valorization 162
 12 vasculatures 162
 12 vituperating 162
 12 volunteering 162
 12 westernising 162
 12 wontednesses 162
 14 Transylvanians 189
 14 supergravities 189
 14 supersonically 189
 14 susceptibility 189
 14 teleportations 189
 14 thermostatting 189
 14 toilsomenesses 189
 14 tranquillizing 189
 14 transitionally 189
 14 treponematosis 189
 14 ultimogeniture 189
 14 ultramodernist 189
 14 uncommonnesses 189
 14 uncrystallized 189
 14 underutilizing 189
 14 unenterprising 189
 14 vaporishnesses 189
 14 victimizations 189
 14 vulcanologists 189
 14 winglessnesses 189
 16 supercompetitive 216
 16 transilluminator 216
 16 transsexualities 216
 16 unconventionally 216
 16 underproductions 216
 16 vasoconstriction 216
 18 uncompromisingness 243
 18 vaingloriousnesses 243
 20 Chrononhotonthologos 270
 
 No odd length words appear as, for example with 3-letter words:
 
 a+b+c = 3*(27) - a - b - c
 
 2(a+b+c)= 3*27
 
 The LHS is even and the RHS is odd. The 3 can be replaced by any odd length and the reasoning is the same.
 
 DefDbl A-Z
 Dim crlf$
 
 
 Private Sub Form_Load()
  Form1.Visible = True
  
  
  Text1.Text = ""
  crlf = Chr$(13) + Chr$(10)
  
  Open "c:\words\words.txt" For Input As #1
  Do
    Line Input #1, l$
    tot1 = 0: tot2 = 0
    For i = 1 To Len(l)
      tot1 = tot1 + InStr("abcdefghijklmnopqrstuvwxyz", LCase(Mid(l, i, 1)))
      tot2 = tot2 + InStr("zyxwvutsrqponmlkjihgfedcba", LCase(Mid(l, i, 1)))
    Next
    If tot1 = tot2 Then
      Text1.Text = Text1.Text & mform(Len(l), "##0") & " "
      Text1.Text = Text1.Text & l & Str(tot1) & crlf
    End If
    DoEvents
  Loop Until EOF(1)
  

  Text1.Text = Text1.Text & crlf & " done"
   
 End Sub


  Posted by Charlie on 2017-02-07 12:51:37
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