Words with Puzzlers

Question

My "friend" (who has absolutely too much time on his hands) made me a DIY Scrabble™ board. He's nice like that. He cut, sanded, painted and even routed out little cradles for the letter tiles.

Oh yeah, and he made letter tiles!

He left it for me as you see below, all filled in and scored on a scoring sheet. I noticed that the letter tiles had no values on them and examined the scoring sheet.

"Gadzooks and Whilakers! Bring me my head gear," I called, oozing masculinity, to my stunning, imaginary wife. "This must be some kind of puzzle for me to solve!"

I slowly, carefully unsheathed my Eagle Black Warrior pencil, sharpened it, and reviewed normal Scrabble™ scoring rules:

• Pink spots are double-word scores
• Red spots are triple-word scores
• Cyan and Blue respectively get double- and triple-letter scores.
• Simultaneous word multipliers get applied in succession
• Tiles that are already on the board which are used to make a new word (indicated by parentheses on the score sheet) get their unadulterated score (no letter- or word-multipliers are applied)
• Unlike normal Scrabble™, no bonus is applied for using 7 tiles in one turn.

Knowing my friend as intimately as I do, he probably wants me to discover the following:

1. What are the values for each^† of the letters?

2. What rule was used as the basis for assigning value to each letter?

3. Super-Secret Hidden BONUS: (2 words)

---

---

---

Scoring Sheet:

1.  STEIN             42            16. DI(M)             48
2.  (S)HRIMP          36            17. (P)ARA(NORMAL)    60
3.  (P)AT             16            18. (D)EL             18
4.  PLA(T)INUM       270            19. (L)EAVE           42
5.  (U)NITS           46            20. E(N)               9
6.  NITROU(S)         94            21. CO(P)PER          43
7.  (N)ORMAL          36            22. REA(C)TION        43
8.  (M)END            22            23. TAB(L)E           45
9.  TAUGH(T)          26            24. DIAGRA(M)        104
10. (T)AP             14            25. (A)CTIVE          30
11. EUREK(A)          72            26. ARS(E)NIC        123
12. (R)ARE            22            27. (E)LECTRON        71
13. APT (AE)          22            28. (T)ONGUE          86
14. TRE(E)            35            29. (TONGUES)STUN     67
15. MEE(T)            22            30. (G)ALAXY          86
                                    31. ZINC(Y)           93  

---

_{† The letters F,J,Q,W are not on the board, but their values must be determined for a complete solution.}

---

Answer 1

[Extremely partial answer. Seems sufficient to be worth posting, though. Still contemplating.]

Letter values (part 1)

We have

a big pile of simultaneous equations to solve. I confess that I got my computer to do it. The results are as follows:
$\begin{array} \\ A:2 && B:4 && C:6 && D:10 && E:2 \\ F:\,? && G:3 && H:1 && I:3 && J:\,? \\ K:10 && L:3 && M:3 && N:7 && O:8 \\ P:6 && Q:\,? && R:9 && S:5 && T:4 \\ U:11 && V:5 && W:\,? && X:2z-3 && Y:15-z \end{array}$
where $z$ is the value of $Z$: so X,Y,Z could be 5,14,1; 7,13,2; 9,12,3; 11,10,4; ...; 31,1,14.

Where do they come from?

I don't know yet. I have dark suspicions that

chemistry is involved, and that perhaps the secret two words might be PERIODIC TABLE (look at all those elements on the board! see how H=1 and C=6, and try to overlook the values of N,O,P,S,K,I,V!) [EDITED to add:] D'oh, evidently I was right to be looking at H and C ... and I'm not sure what variety of brain-failure made me think N and O were problems. Well done to Reinier for seeing what I missed there; go upvote his answer.

but my concrete reasons for thinking so are mostly nonsense, and the details mostly fail to check out.

Presumably once their origin is made clear, the values of FJQW will be obvious.

Some further notes on hidden things on the board:

DIM/MEET/TREE MEND/DEL/LEAVE (Dmitri Mendeleev) -- perhaps these are the super-secret words.
Obvious elements: arsenic, copper, platinum, zinc(y), nitrogen (well, nitrous). Not quite so obvious: TONGUES/STUN.
Other chemistry-themed things: REACTION, ELECTRON.
TABLE.
There's RARE but not EARTH; maybe coincidence.

Answer 2

Partial answer, using the findings of Gareth McCaughan

As Gareth McCaughan already expected,

the periodic table is used in finding the values of the letters. For each letter, the first element which symbol contains this letter is used. Then the digit sum of the atom number is taken, which is the value of the letter. (So for A, the first element is Na, with atom number 11, so the value is $1+1 = 2$.) We get the following results:

A Na 11 2
B Be 4  4
C C  6  6
D Pd 46 10
E He 2  2
F F  9  9
G Mg 12 3
H H  1  1
I Li 3  3
J ??
K K  19 10
L Li 3  3
M Mg 12 3
N N  7  7
O O  8  8
P P  6  6
Q ??
R Ar 18 9
S Si 14 5
T Ti 22 4
U Cu 29 11
V V  23 5
W W  74 11
X Xe 54 9
Y Y  39 12
Z Zn 30 3

These values completely agree with the values found by Gareth McCaughan. However, there is still a problem:

There are namely no element symbols containing J and Q (or I looked over them), so something else has to be done to find their values.