Every letter of the alphabet is given a nonzero numerical value which need not be an integer. The value of a word is the product of the values of its letters. For example, if c=2, a=4, and t=3, then "cat" has the value 2*4*3=24.

Suppose that every pair of homophones has equal values (thus, ate=eight, implying a=igh).

Show that every letter of the alphabet has value 1.

I don't know if there is any other way to show it other than brute force, but here goes. I hope all these words are legal and truly homophones:

be = bee
e = be/be = 1

tea = tee
a = tee/te = e = 1

ail = ale
i = ale/al = e = 1

aunt = ant
u = ant/ant = 1

overdo = overdue
o = overdue/overd = ue = 1

byte = bite
y = bite/bte = i = 1

So all the vowels are 1.

won = one
w = one/on = e = 1

ball = bawl
L = bawl/bal = w = 1

banned = band
n = band/baned = 1/e = 1

barred = bard
r = bard/bared = 1/e = 1

bass = base
s = base/bas = e = 1

daze = days
z = days/dae = ys/e = 1

matte = mat
t = mat/mate = 1/e = 1

chord = cord
h = cord/cord = 1

cite = site
c = site/ite = s = 1

ark = arc
k = arc/ar = c = 1

ducked = duct
d = duct/ducke = t/ke = 1

queue = cue
q = cue/ueue = c/ue = 1

flex = flecks
x = flecks/fle = cks = 1
OR
coax = cokes
x = cokes/coa = kes/a = 1
(I wasn't sure if one of those homonyms would be contested)

appetite = apatite
p = apatite/apetite = a/e = 1

faze = phase
f = phase/aze = phs/z = 1

immerge = emerge
m = emerge/imerge = e/i = 1

right = write
g = write/riht = we/h = 1

jeans = genes
j = genes/eans = ge/a = 1

jamb = jam
b = jam/jam = 1

The one I’m really not sure about is for v. I don’t know if they are truly homonyms.

plaintive = plaintiff
v = plaintiff/plaintie = ff/e = 1

Posted by nikki on 2005-01-18 21:22:21