perplexus.info :: Word Problems : Homophonic Equality

Homophonic Equality (Posted on 2005-01-18)

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.

Submitted by David Shin

Rating: 5.0000 (1 votes)

Solution: (Hide)

Each line is labeled by the letter it proves is equal to 1:

b: lamb, lam
d: ad, add
e: be, bee
f: ef, eff
k: sac, sack
l: bel, bell
n: dam, damn
o: to, too
r: earing, earring
s: es, ess
t: but, butt

a: tea, tee
i: stair, stare
m: dammed, damned
u: some, sum
w: all, awl

c: cee, sea
h: air, heir
q: racket, racquet
v: tav, taw
y: drier, dryer

g: sleigh,slay
x: locks, lox
z: czar, tsar

j: gene, jean
p: phase, faze

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: edu	Charles Walker	2022-08-19 02:40:30
edu	Hanna Edwards	2021-04-28 00:44:12
whaaaaattt????	Andy	2005-05-10 20:21:21
Still need to prove v=1...	David Shin	2005-01-25 19:27:02
re: Homonym verification	DJ	2005-01-19 19:24:47
First Thoughts	DJ	2005-01-19 19:13:53
No Subject	geegee	2005-01-19 13:03:06
re: Homonym verification	nikki	2005-01-18 22:30:24
Homonym verification	David Shin	2005-01-18 21:38:24
Brute force	nikki	2005-01-18 21:22:21

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