Re: Teaser 2505

[Cactus]

Sunday Times Teaser 2505 by Quentin Fowler
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I have given numeric values to 15 letters of the alphabet, not all
positive, not all integral and not all different. Four have the same
positive value. The value of words is the sum of their letter values
and the words ONE, TWO, ..., SEVENTEEN have the values 1, 2, ..., 17
respectively. What is the value of NOUGHT?.

[Guy]

Greetings

Not sure that this is correct, but assuming zero is a positive value
(?) then I'm getting NOUGHT to be 14.625

e 0
f 2.5
g 4.375
h -1.875
i 0
l 4
n 4.5
o -3.5
r -0.625
s 0
t 5.5
u 5.625
v 2.5
w 0
x 6

[Claude]

Hi Guy

I am getting NOUGHT = 19 with:

O = -7/2
N = 9/2
E = 0
T = 11/2
W = 0
H = 5/2
R = -5
F = 5/2
U = 10
I = 0
V = 5/2
S = 0
X = 6
G = 0
L = 4

so NOUGHT = 9/2 -7/2 + 10 + 0 + 5/2 + 11/2 = 19

Seen mostly to agree with you apart from several letters.

Claude

[Garry]

Hello all

The 17 equations in 15 unknowns do not have a unique solution - 11 of
the unknowns have a fixed value, the other 4 can vary. Giving one of
these an arbitrary value x:

E 0
F 5/2
G 5/2 - x
H x
I 0
L 4
N 9/2
O -7/2
R -5/2 - x
S 0
T 11/2
U 15/2 + x
V 5/2
W 0
X 6

Only one value of x gives the required 4 equal positive values amomg
the 15, from which the value of NOUGHT follows ...

Garry

[Cactus]

On Sep 26, 12:31 pm, Garry <dly3...@yahoo.co.uk> wrote:

Hi Guy, Garry and Geoff,

I get:
E = 0
F = 2.5
G = 7.5
H = - 5
I = 0
L = 4
N = 4.5
O = -3.5
R = 2.5
S = 0
T = 5.5
U = 2.5
V = 2.5
W = 0
X = 6

giving four values of 2.5 and NOUGHT as 11.5.

Brian

[Garry]

Hi Brian

Yes I agree, if my x has the value -5 then everything corresponds to
your solution.

Garry

[Teasemaster]

Hi folks
Just catching up after a holuday...
I think this was quite straightforward, and didn't need a total
solution, or even all the information.
SIXTEEN = SIX + TEN +E; E=0
THIRTEEN = THREE + TE(E)N, THIR = THR; I=0
NOUGHT = EIGHT - EI + NOU = 9+U
FIV(E) = FIF; F=V
ON = 1
U = 4-FOR = 4-VOR = 5+R-VN = 5+R-(SVN)+2 = 7-(SVN)+R = R; U = R
NOUGHT = 9+R
FIVE = V+V = 5; V = F = 2.5
NINE = N+N = 9; N = 4.5
S+V+N = 7; S=0
SIX = X; X=6
O+N = 1; O=-3.5
ELEVEN = L+V+N; L = 4
TWELVE = T+W+L+V; T+W = 5.5 (also T+W = TWO-(-3.5) = 5.5)
FOUR = U+R+2.5-3.5; U+R = 5; U = R = 2.5
NOUGHT = 9 + 2.5 = 11.5

TM