This problem has been vexing me all day. It comes from an old IQ test. Note that while the test says not to discuss the problems on it in order to maintain its integrity, the test itself closed years ago so this shouldn't matter now. I have managed to narrow it down decisively to 4 possible solutions.

Each letter has an associated numerical value attached to it, and the total of all the letters equals the physicist’s total value. For example, if the letters G, L, A, S, E, and R had the values 12, 7, 9, 14, 21, and 5, respectively, American physicist Glaser would have a numerical value of 68.

Your objective is to figure out what the last physicist—Feynman—should be valued.

Physicist	Value		Physicist	Value
ROENTGEN	104		PERRIN	98
LORENTZ	102		RICHARDSON	155
CURIE	69		HEISENBERG	118
MICHELSON	109		SCHRODINGER	168
LIPPMAN	88		CHADWICK	114
MARCONI	90		ANDERSON	127
KAMERLINGH	120		DAVISSON	103
PLANCK	96		FERMI	57
STARK	60		STERN	70
EINSTEIN	94		BLOCK	73
BOHR	47		ZERNIKE	99
MILLIKAN	103		CHERENKOV	109
SIEGBAHN	87		FEYNMAN	?

I've gotten what I thought was the hard part out of the way; that is, I did some matrix witchcraft using an online calculator (this is just a massive linear systems of equations problem) to find the value of all the letters used here... except for "y", which appears only in "Feynman." As it turns out, finding y is the real challenge here.

Each letter has a different value. Here are the letters assigned to each value, in order of value:

There are known letters with values 2-24, with one exception (19). I think it's safe to assume that the values start at 1 and end at 26, because there are 26 letters in the alphabet. Since every letter has a different value, I suspect that Y is either 1, 19, 25, or 26.

I've read through every message board on the internet that has this problem. None of them have explained the solution, but one of them seemed to have a user who knew the solution but refused to divulge it. He said the following:

Besides,are you sure there isn't room for something like TWO independent (but consistent) systems of equations with juggled integers values regarding alphabetical order ?
Fact that choice of value for "Y" isn't logically clear / unique is good enough sign for suspicious minds.

In another post:

There are mathematically consistent system & subsystems of lin. eq.+
logically implemented subsystem to the puzzle.
Alltogather they generate unique solution ,which isn't 94.
One side of the puzzle people here realized fine,but another part seems they didn't.

I don't exactly follow him. From what I know of matrices, there is either exactly one solution, infinitely many solutions, or no solution to large systems of equations like these. So the concept of this equation having another unique set of solutions doesn't make sense in my opinion.

One more thing: I don't think it's without significance that when the letters and their values are lined up in order of value, all five vowels appear in a row. Y is "sometimes" a vowel. Is this a clue?