perplexus.info :: Just Math : Yankee dollar

Yankee dollar (Posted on 2014-06-06)

If
IT*IRK+KLM=TRUE
and
7844$ is a common English word
and
in the above coding distinct digits are represented by distinct letters

then

What letters might be represented by the dollar sign ($)?

Rem1: No acronyms, plurals, proper names, esoteric words.

Rem2: Although there are numerous solutions of the alphametic equation, there exist quite a few candidates for ($) (i.e. the last letter of the common word), with a certain letter (which?) dominating the set.

No Solution Yet Submitted by Ady TZIDON

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computer aided solution

| Comment 2 of 9 |

DefDbl A-Z

Dim crlf$

Private Sub Form_Load()

Text1.Text = ""

crlf$ = Chr(13) + Chr(10)

Form1.Visible = True

DoEvents

'itrklmue

a$ = "1234567890": h$ = a$

it = Val(Left(a$, 2))

irk = 100 * (it \ 10) + Val(Mid(a$, 3, 2))

klm = Val(Mid(a$, 4, 3))

truev = 1000 * (it Mod 10) + Val(Mid(a$, 3, 1) + Mid(a$, 7, 2))

If it * irk + klm = truev Then

i = it \ 10

t = it Mod 10

r = (irk \ 10) Mod 10

k = irk Mod 10

l = (klm \ 10) Mod 10

m = klm Mod 10

u = (truev \ 10) Mod 10

e = truev Mod 10

good = 1: w$ = ""

For j = 1 To 4

dig = Val(Mid("7844", j, 1))

didone = 0

If i = dig Then w$ = w$ & "i": didone = 1

If t = dig Then w$ = w$ & "t": didone = 1

If r = dig Then w$ = w$ & "r": didone = 1

If k = dig Then w$ = w$ & "k": didone = 1

If l = dig Then w$ = w$ & "l": didone = 1

If m = dig Then w$ = w$ & "m": didone = 1

If u = dig Then w$ = w$ & "u": didone = 1

If e = dig Then w$ = w$ & "e": didone = 1

If didone = 0 Then good = 0: Exit For

Next j

If good Then

If Mid(a$, 9, 1) < Right(a$, 1) Then

Text1.Text = Text1.Text & w$ & Str(it) & Str(irk) & Str(klm) & Str(truev) & crlf: DoEvents

End If

permute a$

Loop Until a$ = h$

Text1.Text = Text1.Text & "done"

End Sub

finds

7844 IT*IRK+KLM=TRUE
kull 12 137 745 2389
kemm 12 137 754 2398
lmrr 12 146 678 2430
elrr 12 146 685 2437
mlrr 12 146 687 2439
urll 12 186 643 2875
mlrr 26 241 187 6453
tlkk 27 264 481 7609
tlkk 27 264 485 7613
tekk 27 264 490 7618
tumm 27 265 534 7689
tell 27 265 543 7698
rtmm 28 279 904 8716
rtll 28 279 941 8753
mtll 28 296 647 8935
kemm 12 107 754 2038

I'd say

tumm 27 265 534 7689

leads to the word tummy so that $ = Y.

Posted by Charlie on 2014-06-06 16:54:21

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