perplexus.info :: Word Problems : Star Stare

Star Stare (Posted on 2008-07-16)


           !
          / \
     !---!---!---!
      \ /     \ /
       !       W
      / \     / \
     !---!---!---!
          \ /
           !

Each intersection of this hexagonal star is the location of a unique letter none of which is an "A". A "W" is already placed as a starter.

Each line is a common English four letter word when read from at least one direction.

What solutions can you offer?

An afterthought:
Using unique letters, but with access to all vowels, what other solutions are available?

See The Solution Submitted by brianjn

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computer solutions

| Comment 2 of 10 |

Four files were used: lists of 4-letter words sorted by first letter, sorted by second letter, third letter, and by last letter.

A table is kept of the beginning and end record positions of each letter of the alphabet in each of the four files.

Dim startOf(4, 26), endOf(4, 26), abet
Dim p1$, p2$, p3$, p4$, p5$, p6$, p7$, p8$, p9$, p10$, p11$, p12$, used$

Private Sub cmdStart_Click()
FontTransparent = False
FontName = "courier new"
p7$ = "w"
used$ = "a"
Open "words41.txt" For Binary As #1
Open "words42.txt" For Binary As #2
Open "words43.txt" For Binary As #3
Open "words44.txt" For Binary As #4
Open "star stare.txt" For Output As #5

abet = "abcdefghijklmnopqrstuvwxyz"

nWords = LOF(1) / 4

w$ = Space$(4)
For i = 1 To nWords
   Get #1, i * 4 - 3, w$
   If Left(w$, 1) <> pStart Then
    letNo = InStr(abet, Left$(w$, 1))
    startOf(1, letNo) = i
    If letNo > 1 Then endOf(1, InStr(abet, pStart)) = i - 1
    pStart = Left(w$, 1)
   End If
   endOf(1, InStr(abet, pStart)) = nWords
Next

w$ = Space$(4)
For i = 1 To nWords
   Get #2, i * 4 - 3, w$
   If Mid(w$, 2, 1) <> pStart Then
    letNo = InStr(abet, Mid(w$, 2, 1))
    startOf(2, letNo) = i
    If letNo > 1 Then endOf(2, InStr(abet, pStart)) = i - 1
    pStart = Mid(w$, 2, 1)
   End If
   endOf(2, InStr(abet, pStart)) = nWords
Next

w$ = Space$(4)
For i = 1 To nWords
   Get #3, i * 4 - 3, w$
   If Mid(w$, 3, 1) <> pStart Then
    letNo = InStr(abet, Mid(w$, 3, 1))
    startOf(3, letNo) = i
    If letNo > 1 Then endOf(3, InStr(abet, pStart)) = i - 1
    pStart = Mid(w$, 3, 1)
   End If
   endOf(3, InStr(abet, pStart)) = nWords
Next

w$ = Space$(4)
For i = 1 To nWords
   Get #4, i * 4 - 3, w$
   If Mid(w$, 4, 1) <> pStart Then
    letNo = InStr(abet, Mid(w$, 4, 1))
    startOf(4, letNo) = i
    If letNo > 1 Then endOf(4, InStr(abet, pStart)) = i - 1
    pStart = Mid(w$, 4, 1)
   End If
   endOf(4, InStr(abet, pStart)) = nWords
Next

For i = 1 To 4: For j = 1 To 26
   If startOf(i, j) = 0 Then startOf(i, j) = 1
   If endOf(i, j) = 0 Then endOf(i, j) = 1
Next: Next

For dir1 = 2 To 3
    DoEvents
    ix = InStr(abet, "w")
    For s1 = startOf(dir1, ix) To endOf(dir1, ix)
     Get #dir1, s1 * 4 - 3, w$
     If noRept(Left(w$, dir1 - 1) + Right(w$, 4 - dir1)) Then
      w1$ = w$
      If dir1 = 2 Then
       p11$ = Mid(w$, 1, 1): p4$ = Mid(w$, 3, 1): p1$ = Mid(w$, 4, 1):
      Else
       p1$ = Mid(w$, 1, 1): p4$ = Mid(w$, 2, 1): p11$ = Mid(w$, 4, 1):
      End If
      used$ = used$ + p1$ + p4$ + p7$ + p11$

For dir2 = 2 To 3
    DoEvents
    ix = InStr(abet, p4$)
    For s2 = startOf(dir2, ix) To endOf(dir2, ix)
     Get #dir2, s2 * 4 - 3, w$
     If noRept(Left(w$, dir2 - 1) + Mid(w$, dir2 + 1)) Then
      w2$ = w$
      If dir2 = 2 Then
       p5$ = Mid(w$, 1, 1): p3$ = Mid(w$, 3, 1): p2$ = Mid(w$, 4, 1):
      Else
       p2$ = Mid(w$, 1, 1): p3$ = Mid(w$, 2, 1): p5$ = Mid(w$, 4, 1):
      End If
      used$ = used$ + p2$ + p3$ + p5$

For dir3 = 1 To 4 Step 3
    ix = InStr(abet, p1$)
    For s3 = startOf(dir3, ix) To endOf(dir3, ix)
     Get #dir3, s3 * 4 - 3, w$
     If Mid(w$, (5 + dir3) / 3, 1) = p3$ Then
        If noRept(Mid(w$, (11 - dir3 * 2) / 3, 2)) Then
         w3$ = w$
         If dir3 = 1 Then
          p8$ = Mid(w$, 4, 1): p6$ = Mid(w$, 3, 1)
         Else
          p6$ = Mid(w$, 2, 1): p8$ = Mid(w$, 1, 1)
         End If
         used$ = used$ + p6$ + p8$
         DoEvents

For dir4 = 1 To 4 Step 3
    ix = InStr(abet, p2$)
    For s4 = startOf(dir4, ix) To endOf(dir4, ix)
     Get #dir4, s4 * 4 - 3, w$
     If Mid(w$, (5 + dir4) / 3, 1) = p6$ Then
        If noRept(Mid(w$, (11 - dir4 * 2) / 3, 2)) Then
         w4$ = w$
         If dir4 = 1 Then
          p9$ = Mid(w$, 3, 1): p12$ = Mid(w$, 4, 1)
         Else
          p9$ = Mid(w$, 2, 1): p12$ = Mid(w$, 1, 1)
         End If
         used$ = used$ + p9$ + p12$

For dir5 = 1 To 4 Step 3
    ix = InStr(abet, p8$)
    For s5 = startOf(dir5, ix) To endOf(dir5, ix)
     Get #dir5, s5 * 4 - 3, w$
     If Mid(w$, (5 + dir5) / 3, 1) = p9$ And Mid(w$, 5 - dir5, 1) = p11$ Then
        If noRept(Mid(w$, (10 - dir5) / 3, 1)) Then
         w5$ = w$
         If dir5 = 1 Then
          p10$ = Mid(w$, 3, 1)
         Else
          p10$ = Mid(w$, 2, 1)
         End If
         used$ = used$ + p10$

If isWord(p12$ + p10$ + p7$ + p5$) Then
    CurrentX = 1: CurrentY = 1
    Print #5, w1$: Print #5, w2$: Print #5, w3$: Print #5, w4$: Print #5, w5$
    Print #5, p12$ + p10$ + p7$ + p5$
    Print #5,
    Print w1$: Print w2$: Print w3$: Print w4$: Print w5$
    Print p12$ + p10$ + p7$ + p5$
    Print
    DoEvents
End If
If isWord(p5$ + p7$ + p10$ + p12$) Then
    CurrentX = 1: CurrentY = 1
    Print #5, w1$: Print #5, w2$: Print #5, w3$: Print #5, w4$: Print #5, w5$
    Print #5, p5$ + p7$ + p10$ + p12$
    Print #5,
    Print w1$: Print w2$: Print w3$: Print w4$: Print w5$
    Print p5$ + p7$ + p10$ + p12$
    Print
    DoEvents
End If

         ix = InStr(used$, p10$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
        End If
     End If
    Next
Next dir5

         ix = InStr(used$, p9$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
         ix = InStr(used$, p12$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
        End If
     End If
    Next
Next dir4

         ix = InStr(used$, p6$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
         ix = InStr(used$, p8$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
        End If
     End If
    Next
Next dir3

      ix = InStr(used$, p2$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
      ix = InStr(used$, p3$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
      ix = InStr(used$, p5$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
     End If
    Next
Next dir2

      ix = InStr(used$, p1$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
      ix = InStr(used$, p4$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
      ix = InStr(used$, p7$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
      ix = InStr(used$, p11$): used$ = Left(used$, ix - 1) + Mid(used$, ix + 1)
     End If
    Next
Next dir1
End Sub

Function noRept(x$)
good = 1
For i = 1 To Len(x$)
If InStr(Mid(x$, i + 1), Mid(x$, i, 1)) > 0 Then good = 0: Exit For
If InStr(used$, Mid(x$, i, 1)) > 0 Then good = 0: Exit For
Next
noRept = good
End Function

Function isWord(w$)
wChk$ = Space$(4)
v = False
For i = startOf(1, InStr(abet, Left(w$, 1))) To endOf(1, InStr(abet, Left(w$, 1)))
Get #1, i * 4 - 3, wChk$
If wChk$ = w$ Then v = True
Next
isWord = v
End Function

The word lists below were produced by the above program. Those involving unusual words were eliminated manually. The diagrams to the right of each were added by another program:


owed            d
term         m r e t
surd          u   w
glum         s l i o
oils            g
twig

swig            g
lien         n e i l
dreg          r   w
burn         d u o s
duos            b
bowl

swig            g
dint         t n i d
hung          u   w
lout         h o e s
hoes            l
lewd

twig            g
lien         n e i l
gems          m   w
hymn         s y o t
toys            h
howl

twig            g
silk         k l i s
glen          e   w
kerb         n r o t
torn            b
bows

twig            g
silk         k l i s
glen          e   w
kerb         n r o t
torn            b
swob

twig            g
oils         s l i o
glum          u   w
surd         m r e t
term            d
owed

twig            g
sine         e n i s
bung          u   w
clue         b l o t
blot            c
cows

twig            g
sine         e n i s
dung          u   w
blue         d l o t
told            b
bows

twig            g
sine         e n i s
dung          u   w
blue         d l o t
told            b
swob

twig            g
sine         e n i s
dung          u   w
clue         d l o t
told            c
cows

twig            g
sire         e r i s
grub          u   w
clue         b l o t
blot            c
cows

twin            n
sire         e r i s
burn          u   w
clue         b l o t
blot            c
cows

swob            b
told         d l o t
blue          u   w
dung         e n i s
sine            g
twig

swob            b
torn         n r o t
kerb          e   w
glen         k l i s
silk            g
twig

swob            b
loud         d u o l
bunt          n   w
mind         t i e s
ties            m
mewl

swob            b
lout         t u o l
burp          r   w
trim         p i e s
pies            m
mewl

swob            b
lout         t u o l
drub          r   w
trim         d i e s
dies            m
mewl

swob            b
lion         l i o n
bird          r   w
hurl         d u e s
dues            h
hewn

swob            b
lion         l i o n
crib          r   w
hurl         c u e s
cues            h
hewn

swop            p
loud         d u o l
punt          n   w
mind         t i e s
ties            m
mewl

swop            p
lion         l i o n
drip          r   w
hurl         d u e s
dues            h
hewn

twos            s
cloy         c l o y
slum          u   w
curd         m r e t
term            d
dewy

twos            s
ploy         p l o y
slim          i   w
drip         m r e t
term            d
dewy

twos            s
ploy         p l o y
mils          i   w
drip         m r e t
term            d
dewy

swum            m
yurt         t r u y
form          o   w
told         f l e s
self            d
dewy

swum            m
gout         g o u t
prom          r   w
grin         p i e s
pies            n
newt

lewd            l
foes         f o e s
loin          i   w
firm         n r u d
durn            m
swum

lewd            l
hoes         h o e s
lout          u   w
hung         t n i d
dint            g
swig

bowl            b
muon         m u o n
buys          y   w
myth         s t e l
lets            h
hewn

cowl            c
mhos         m h o s
chit          i   w
mind         t n e l
lent            d
dews

fowl            f
norm         m r o n
turf          u   w
mush         t s e l
lest            h
hewn

fowl            f
pros         p r o s
turf          u   w
puny         t n e l
lent            y
yews

howl            h
toys         s y o t
hymn          m   w
gems         n e i l
lien            g
twig

mewl            m
dies         d i e s
prim          r   w
drub         p u o l
loup            b
swob

mewl            m
dies         d i e s
trim          r   w
drub         t u o l
lout            b
bows

mewl            m
dies         d i e s
trim          r   w
drub         t u o l
lout            b
swob

mewl            m
dies         d i e s
trim          r   w
curd         t u o l
lout            c
cows

mewl            m
pies         p i e s
trim          r   w
burp         t u o l
lout            b
bows

mewl            m
pies         p i e s
trim          r   w
burp         t u o l
lout            b
swob

mewl            m
ties         t i e s
mind          n   w
bunt         d u o l
loud            b
bows

mewl            m
ties         t i e s
mind          n   w
bunt         d u o l
loud            b
swob

mewl            m
ties         t i e s
mind          n   w
punt         d u o l
loud            p
pows

mewl            m
ties         t i e s
mind          n   w
punt         d u o l
loud            p
swop

mewl            m
ties         t i e s
mind          n   w
runt         d u o l
loud            r
rows

hewn            h
lest         t s e l
mush          u   w
turf         m r o n
norm            f
fowl

hewn            h
lets         s t e l
myth          y   w
buys         m u o n
muon            b
bowl

hewn            h
cues         c u e s
hurl          r   w
crib         l i o n
lion            b
bows

hewn            h
cues         c u e s
hurl          r   w
crib         l i o n
lion            b
swob

hewn            h
dues         d u e s
hurl          r   w
drip         l i o n
lion            p
pows

hewn            h
dues         d u e s
hurl          r   w
drip         l i o n
lion            p
swop

hewn            h
dues         d u e s
hurl          r   w
drip         l i o n
noil            p
pows

hewn            h
dues         d u e s
hurl          r   w
bird         l i o n
lion            b
bows

hewn            h
dues         d u e s
hurl          r   w
bird         l i o n
lion            b
swob

town            t
mhos         m h o s
thug          u   w
plum         g l e n
glen            p
pews

town            t
rhos         r h o s
thug          u   w
ruly         g l e n
glen            y
yews

bows            b
told         d l o t
blue          u   w
dung         e n i s
sine            g
twig

bows            b
torn         n r o t
kerb          e   w
glen         k l i s
silk            g
twig

bows            b
loud         d u o l
bunt          n   w
mind         t i e s
ties            m
mewl

bows            b
lout         t u o l
burp          r   w
trim         p i e s
pies            m
mewl

bows            b
lout         t u o l
drub          r   w
trim         d i e s
dies            m
mewl

bows            b
lion         l i o n
bird          r   w
hurl         d u e s
dues            h
hewn

bows            b
lion         l i o n
crib          r   w
hurl         c u e s
cues            h
hewn

cows            c
told         d l o t
clue          u   w
dung         e n i s
sine            g
twig

cows            c
loup         p u o l
curd          r   w
prim         d i e s
dies            m
mewl

cows            c
lout         t u o l
curd          r   w
trim         d i e s
dies            m
mewl

cows            c
blot         b l o t
clue          u   w
bung         e n i s
sine            g
twig

cows            c
blot         b l o t
clue          u   w
burn         e r i s
sire            n
twin

cows            c
blot         b l o t
clue          u   w
grub         e r i s
sire            g
twig

dews            d
lent         t n e l
mind          i   w
chit         m h o s
mhos            c
cowl

dews            d
lent         t n e l
rind          i   w
chit         r h o s
rhos            c
cowl

mows            m
ploy         p l o y
film          i   w
drip         f r e s
serf            d
dewy

pews            p
glen         g l e n
plum          u   w
thug         m h o s
mhos            t
town

pows            p
loud         d u o l
punt          n   w
mind         t i e s
ties            m
mewl

pows            p
lion         l i o n
drip          r   w
hurl         d u e s
dues            h
hewn

rows            r
loud         d u o l
runt          n   w
mind         t i e s
ties            m
mewl

yews            y
lend         d n e l
puny          u   w
crud         p r o s
pros            c
cowl

yews            y
lent         t n e l
puny          u   w
turf         p r o s
pros            f
fowl

yews            y
next         t x e n
pixy          i   w
grit         p r o s
pros            g
gown

newt            n
pies         p i e s
grin          r   w
prom         g o u t
gout            m
swum

dewy            d
self         f l e s
told          o   w
form         t r u y
yurt            m
swum

dewy            d
serf         f r e s
drip          i   w
film         p l o y
ploy            m
mows

dewy            d
term         m r e t
drip          i   w
mils         p l o y
ploy            s
twos

dewy            d
term         m r e t
drip          i   w
slim         p l o y
ploy            s
twos

dewy            d
term         m r e t
curd          u   w
slum         c l o y
cloy            s
twos

dewy            d
bren         b r e n
curd          u   w
slub         c l o y
cloy            s
sown

Posted by Charlie on 2008-07-16 15:40:41

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