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 Test #5 (Posted on 2014-08-31)
Let us assign the name Tes letters to the letters of the word test i.e. t,e,s.
Consider the quantity P of Tes letters as percentage of the word's length.
Thus P(set)= 100%
P(best)=75%
P(resistor)=50%

P(settee)=100%
P(estimates)=66% etc
If Pmx(n) represents the maximal value of P for a word of n letters, - there exist trivial samples for n=3,4,5,6,7 i.e. set,test,tests,settee,settees - they all comply with Pmx(n)=1.

Please provide the values of Pmx for words of 8,9, ....20 letters.

Elligible: words appearing in reputable dictionary, including derivatives like plurals, verbs in 3rd person et al.

 See The Solution Submitted by Ady TZIDON No Rating

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 computer findings Comment 1 of 1
In some cases below, some ratios lower than the maximum have been included so as to give a greater choice in what may be deemed common words. When only one ratio is shown, it it the maximum. Sort order for those with more than one shown ratio, are ratio increasing major and alphbetic by word minor.

All values are expressed as a fraction, rather than a percent.

8
0.87500000  assesses
0.87500000  estheses
0.87500000  esthetes
0.87500000  septette
0.87500000  sextette
0.87500000  steepest
0.87500000  stresses
0.87500000  sweetest
0.87500000  testates
0.87500000  testiest

9
0.88888889  seeresses
0.88888889  septettes
0.88888889  sextettes

10
0.80000000  esthesises
0.80000000  meetnesses
0.80000000  reassesses
0.80000000  restresses
0.80000000  statuettes
0.80000000  stressless
0.80000000  teentsiest

11
0.72727273  assessments
0.72727273  densenesses
0.72727273  electresses
0.72727273  erectnesses
0.72727273  fleetnesses
0.72727273  messinesses
0.72727273  metestruses
0.72727273  pettinesses
0.72727273  prestresses
0.72727273  priestesses
0.72727273  repossesses
0.72727273  seedinesses
0.72727273  settlements
0.72727273  sexlessness
0.72727273  sheernesses
0.72727273  sleeknesses
0.72727273  stalenesses
0.72727273  stepsisters
0.72727273  sternnesses
0.72727273  stoutnesses
0.72727273  tastinesses
0.72727273  tattinesses
0.72727273  temptresses
0.72727273  tessellates
0.72727273  testcrosses
0.72727273  tritenesses
0.72727273  typesetters
0.72727273  uselessness
0.81818182  steepnesses
0.81818182  sweetnesses
0.81818182  tensenesses
0.81818182  tersenesses
0.81818182  testinesses

12
0.75000000  astutenesses
0.75000000  effetenesses
0.75000000  petitenesses
0.75000000  restlessness
0.75000000  seamstresses
0.75000000  sedatenesses
0.75000000  selectnesses
0.75000000  sempstresses
0.75000000  serenenesses
0.75000000  severenesses
0.75000000  steelinesses
0.75000000  sveltenesses

13
0.69230769  agelessnesses
0.69230769  artlessnesses
0.69230769  austerenesses
0.69230769  betweennesses
0.69230769  blessednesses
0.69230769  ceaselessness
0.69230769  destituteness
0.69230769  earnestnesses
0.69230769  endlessnesses
0.69230769  extremenesses
0.69230769  festivenesses
0.69230769  genteelnesses
0.69230769  gutlessnesses
0.69230769  intensenesses
0.69230769  letterpresses
0.69230769  pettishnesses
0.69230769  possessedness
0.69230769  presentnesses
0.69230769  reassessments
0.69230769  repletenesses
0.69230769  resettlements
0.69230769  restivenesses
0.69230769  saplessnesses
0.69230769  sinlessnesses
0.69230769  sleeplessness
0.69230769  sottishnesses
0.69230769  statelinesses
0.69230769  stiltednesses
0.69230769  stuntednesses
0.69230769  stylelessness
0.69230769  testosterones
0.69230769  toplessnesses
0.69230769  witlessnesses
0.76923077  senselessness
0.76923077  sexlessnesses
0.76923077  statelessness
0.76923077  tastelessness
0.76923077  uselessnesses

14
0.71428571  heedlessnesses
0.71428571  listlessnesses
0.71428571  needlessnesses
0.71428571  resistlessness
0.71428571  seamlessnesses
0.71428571  selflessnesses
0.71428571  spotlessnesses
0.71428571  tactlessnesses
0.71428571  timelessnesses
0.71428571  tirelessnesses
0.71428571  tonelessnesses
0.78571429  restlessnesses
0.78571429  stresslessness

15
0.73333333  ceaselessnesses
0.73333333  destitutenesses
0.73333333  possessednesses
0.73333333  sleeplessnesses
0.73333333  stylelessnesses
0.80000000  senselessnesses
0.80000000  statelessnesses
0.80000000  tastelessnesses

16
0.68750000  detestablenesses
0.68750000  possessivenesses
0.68750000  relentlessnesses
0.68750000  speechlessnesses
0.75000000  resistlessnesses
0.81250000  stresslessnesses

17
0.64705882  exhaustlessnesses
0.64705882  necessitousnesses
0.64705882  remorselessnesses
0.64705882  sententiousnesses
0.64705882  tempestuousnesses
0.70588235  bittersweetnesses
0.70588235  defenselessnesses

18
0.55555556  discontentednesses
0.55555556  expressionlessness
0.55555556  greatheartednesses
0.55555556  inexpressivenesses
0.55555556  intermediatenesses
0.55555556  interrelatednesses
0.55555556  irresistiblenesses
0.55555556  obstreperousnesses
0.55555556  preposterousnesses
0.55555556  propertylessnesses
0.55555556  representativeness
0.55555556  shortsightednesses
0.61111111  ostentatiousnesses
0.61111111  stoutheartednesses

19
0.57894737  heterogeneousnesses
0.57894737  oversensitivenesses
0.57894737  tenderheartednesses
0.63157895  disinterestednesses
0.63157895  structurelessnesses

20
0.45000000  comprehensiblenesses
0.45000000  representationalists
0.45000000  unsatisfactorinesses
0.50000000  extemporaneousnesses
0.50000000  indestructiblenesses
0.50000000  interconnectednesses
0.50000000  nondestructivenesses
0.50000000  overprotectivenesses
0.50000000  unrepresentativeness
0.55000000  hypersensitivenesses
0.60000000  expressionlessnesses
0.60000000  representativenesses

The program was originally written to show only those that made for or matched the latest maximum. This was changed to specific values depending on the size of the word. But even then, some of the lower ratios were deleted manually, after having sorted the output within the word sizes.

DefDbl A-Z
Dim crlf\$

Function mform\$(x, t\$)
a\$ = Format\$(x, t\$)
If Len(a\$) < Len(t\$) Then a\$ = Space\$(Len(t\$) - Len(a\$)) & a\$
mform\$ = a\$
End Function

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For n = 8 To 20
Text1.Text = Text1.Text & crlf & n & crlf
Open "\words\words" + LTrim(Str(n)) + ".txt" For Binary As #1
w\$ = Space\$(n)
maxm = 0
Do
Get #1, , w\$
If EOF(1) Then Exit Do
ct = 0
For i = 1 To Len(w\$)
If InStr("tes", Mid(w\$, i, 1)) Then ct = ct + 1
Next
ratio = ct / n
Select Case n
Case 8, 9
cutoff = 0.75
Case 10, 11, 12, 14, 15
cutoff = 0.7
Case 13, 16
cutoff = 0.65
Case 17, 18, 19
cutoff = 0.5
Case 20
cutoff = 0.4
End Select
If ratio >= cutoff Then
maxm = ratio
Text1.Text = Text1.Text & mform(ratio, "0.00000000") & "  " & w\$ & crlf
DoEvents
End If
Loop
Close 1
Next

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

 Posted by Charlie on 2014-08-31 13:13:28

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