Each of the 26 letters has a secret numerical value, and the value of a word is the sum of the values of its letters.

mwdaly@pobox.com (Matthew Daly) writes:

> The word list is the names of the first 104 chemical elements, from
> hydrogen to unnilquadium.  (You pointed out that there is no "J" in
> this list, but the professor sternly said "You forgot about
> Jermanium!" and you didn't press the issue -- that's your J word..)
> Since this is such a phenominally large list, the professor won't
> give you all of them.  In fact, he will only give you one word per
> minute while the test is running, whichever elements you ask him for.

> The good news is that you know all the details of this challenge
> ahead of time, and can prepare for it.  To give an example, you can
> plan to ask him in the first minute for the value of XENON, and in the
> second minute ask him about NEON, knowing that the difference between
> them is the value of X.

I have a solution using the minimum 26 elements.

In each step, the new element used is in all caps.

ERBIUM
TERBIUM-erbium=T
YTTERBIUM-terbium-T=Y
HELIUM (will use later)
TIN-T=I+N
IRON-(I+N)=O+R
helium+(O+R)-THORIUM=(E+L)
LEAD-(E+L)=A+D
RADON-(O+R)-(A+D)=N
..and tin-N-T=I
helium-LITHIUM+I+T=E
..and (E+L)-E=L
BARIUM-erbium+E=A
..and lead-A-E-L=D
CURIUM-cerium+E=U

[ Editor: two slips here.  helium - thorium = E+L-T-O-R, so the
seventh line also needs a +T (T is already known).  And cerium is
written in lower case as if already asked for, but it is not among the
26 capitalized elements. ]

At this point, we know enough letters that all we need to due is use
elements with one letter unknown, including the ones we hgave already
asked about.  After getting O, I'll go in alphabetical order.

NEON-2N-E=O
..and iron-I-N-O=R
BORON-R-2O-N=B
..and barium-A-B-I-U-R=M
...and helium-E-I-L-M-U=H
CARBON-A-B-N-O-R=C
FLUORINE-E-I-L-N-O-R-U=F
GOLD-D-L-O=G
JERMANIUM-A-E-I-2M-N-R-U=J (sic)
BERKELIUM-B-2E-I-L-M-R-U=K
KRYPTON-K-N-O-R-T-Y=P [Editor: "-P" in the original]
UNNILQUADIUM-A-D-2I-L-M-2N-3U=Q
CESIUM-C-E-I-M-U=S
VANADIUM-2A-D-I-M-N-U=V
LAWRENCIUM-A-C-E-I-L-M-N-R-U=W
XENON-neon=X
ZINC-C-I-N=Z

-- David Grabiner <grabiner@math.lsa.umich.edu>

----------

Matthew Daly (mwdaly@pobox.com) wrote:
: Can you determine a series of elements and mathematical calculations
: that would reasonably enable you to deduce the values of all 26
: letters in a half hour with a desk calculator and the equations
: written out ahead of time?

Cute puzzle.  26 minutes is the theoretical minimum, since you must
have at least 26 equations.  A solution in 26 minutes is given below.
I don't think I used any elements that have transatlantic differences
in spelling, as well.

terbium-erbium: T  (2)
ruthenium-rhenium-T: U (4)
cerium-curium+U: E  (6)
polonium-plutonium+U+T: O  (8)
  We can get the remaining letters one at a time by picking names
  in which only one letter is still unknown:
neon: N  (9)
xenon: X (10)
tin: I (11)
iron: R (12)
boron: B (13)
erbium: M  (reuse, still 13)
curium: C  (reuse, still 13)
iridium: D (14)
sodium: S (15)
cadmium: A (16)
argon: G (17)
gold: L (18)
polonium: P (reuse, still 18)
rhenium: H  (reuse, still 18)
zinc: Z (19)
fluorine: F (20)
yttrium: Y (21)
krypton: K (22)
unnilquadium: Q (23)
silver: V  (24)
lawrencium: W (25)
jermanium: J (26)

-- Lynn Johannesen <lynnj@netcom.com>