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w=f[z]

Extremely difficult question from an IQ test...

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Hi everyone,

Here is a question I first encountered in 2002. It was from the website http://www.highiqsociety.org/.

 

Since then, they have taken the test that had this particular question down.

 

Here is the question:

"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."

 

roentgen 89

lorentz 91

curie 67

michelson 95

lippman 123

marconi 82

kamerlingh 127

planck 77

stark 66

einstein 109

bohr 43

millikan 135

siegbahn 114

 

perrin 78

richardson 115

heisenberg 122

schrodinger 122

chadwick 90

anderson 86

davisson 121

fermi 62

stern 56

block 65

zernike 77

cherenkov 81

feynman ???

 

Note: At first, Planck was spelled "Plank," but the webmaster at the original website stated that "Plank" was a typo (as stated on another forum - see below).

 

Also, there may be some dispute about the spelling of "Block" (Bloch???) and Lippman (Lippmann???).

 

 

Okay... my first thought was that this is an easy problem to solve. Simple linear algebra... right? This has proven to be a real bi*ch though....

 

An old (2002) discussion from another forum about this problem can be found here:

http://episteme.arstechnica.com/eve/forums/a/tpc/f/6330927813/m/6740938424/p/1

Note: No one there solved it either....

 

Apparently 13/30,000 of the people that took this test got the correct answer. I think that number is akin to the odds of getting it correct if everyone simply guessed...!

 

Anyway, I never found a satisfactory solution, and I haven't seriously looked at it for some time now, but for some reason I thought about it last night and thought I'd post it.

 

Some of the things I tried:

(Note: I noted that "y" in "Feynman" was the only place where "y" showed up... so I thought that there must be a recognizable pattern in the way values are assigned to letters.)

- Tried using linear algebra and solving a matrix

- Tried using Mathematica/Maple

- Tried "brute forcing" it with a computer code (until I realized that the code would run for... like a year!)

- Tried equating different names, etc.

- It's been so long now I can't remember what all I tried, but it seems like everything I read in the other forum that they tried, I also tried. But nothing worked for me and I never solved this one.

 

 

So...

Have any of you seen this before? (If so, do you have the solution?)

Care to give it a shot?

 

Cheers,

w=f[z]

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I'll try this one, since I've run out of complicated and interesting ones. But if the typos are in there, I'll also try the variations on the names. Maybe even research to make sure.

I dunno how llong it'll take me. I'll try to update by the end of the week.

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Hi Pre4edgc,

I double checked with my printed version of this problem and everything seems correct (i.e., I copied it correctly).

 

I guess the thing that really bugged me about this problem is that linear algebra should have done the trick. This makes me think there is something more to it....

 

Good luck,

w=f[z]

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If you calculate the average value per letter it works out at about 12.5 which would indicate that the puzzle is playing reasonably fairly. You might consider the spelling and character set used but letters 1-26 would average at 13.5 while 0-25 at 12.5. maybe it is 0 -26 or 1 - 27 with and o with two dots, maybe not.

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I mentioned that I attempted a "brute force" method with a computer code. The problem I had though was that it was going to take a long long time to run (something like 26^{total number of letters to check} - computations). Yeah... not a very efficient programming technique... I know....

 

Anyone out there handy with coding efficient computer codes? There's got to be an efficient way to brute-force this thing... a way to minimize the number of calculations that is....

 

Cheers

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;344336']I mentioned that I attempted a "brute force" method with a computer code. The problem I had though was that it was going to take a long long time to run (something like 26^{total number of letters to check} - computations). Yeah... not a very efficient programming technique... I know....

 

Anyone out there handy with coding efficient computer codes? There's got to be an efficient way to brute-force this thing... a way to minimize the number of calculations that is....

Cheers

The maximum number of possibilities is quite massive' date=' but the number of [i']actual comparisons[/i] needed to check each possibility should generally be very low (because the variable assignments in each round of checking are likely to be wrong and therefore fail the test condition).

 

A recursive function could probably chew through this problem quite quickly if you feed it the right arrays.

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;344209'](Note: I noted that "y" in "Feynman" was the only place where "y" showed up... so I thought that there must be a recognizable pattern in the way values are assigned to letters.)

 

Since they never said there was a bound on the numbers, this would be unsolvable. Y can have any value. One could assume that they are 1-26 and work from that premise, but I don't see an "x" either. How isn't this underconstrained?

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Hi Swansont,

Normally I'd agree with you... "y" seems like a free parameter, but on the original test (which is no longer there...), it seems like it was looking for a number. In other words, it might be tricky to have an automated "IQ test" that can check for a phrase such as "no solution" and/or "unsolvable" and/or "underconstrained" etc., which, if you are correct, would all be correct answers.

 

That lead me to think that we must solve for the letters that are present, and then there must be a recognizable relation in how each letter is assigned a value. Then we would have to deduce the pattern and find y's value.

 

Missing also are j & q (and x as you mentioned). So there really are only 22 letters out of 26 to work with....

 

Cheers,

w=f[z]

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To elaborate on my previous point...

Suppose we assigned the values to the letters as such:

a=1, b=2, c=3, ..., z=26.

 

Then if we had a list of names such that

Bohr = 43 (which matches the original incidentally...)

Curie = 56

etc.

 

If that were the case, it seems like we could find the pattern (even without a complete set) and deduce that Feynman = 78.

 

Sure... strictly speaking, we must agree with swansont in that there is no guarantee that "y" must follow the pattern (in other words, y could be anything). But I would assume (perhaps falsely) that this question would not have that simple of an answer. I would assume that there would be a pattern.

 

 

 

By the way... most online "IQ tests" do have this simple of answers. But this test was meant to be printed out with no time limit or restrictions on methods (e.g., computer coding this problem was perfectly fine with the rules). This test was meant to test people who are "extremely gifted" such that gifted individuals would only score average. It was supposed to test up to IQ 180+. The other questions were not easy either. As a matter of fact, I've seen two others posted here... the "breeding furbles" one, and the "maximum number of 1-in. diameter spheres that can be packed in a box 10 in. square by 5 in. deep...". (The answers to those I got by the way... 1/2 & 594.) I could re-find those if anyone wants....

 

Edit: The name of this test was the "Haselbauer - Dickheiser Test for Exceptional Intelligence" by the way. "Has-Dick" for short. :)

 

Edit #2: Just realized I contradicted myself (sort of). The test could be printed out, and there was no time limit etc., but you had to go back to the website and enter your answers in the online version of the test. That is, it wasn't one of those "mail in with a $15 fee"-type tests.

 

Cheers,

w=f[z]

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The fact that it's under-constrained makes a little sense. It's an IQ test, not a test of programming skills. But not having a time limit means there probably isn't some trick that simplifies it.

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The fact that it's under-constrained makes a little sense. It's an IQ test, not a test of programming skills. But not having a time limit means there probably isn't some trick that simplifies it.

 

That makes sense. But I have to wonder then...

Since one had to enter the answers online, and presumably there is not a live person at the other end checking answers (that would take a lot of effort...), what would you put in for an answer?

 

Cheers

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I did a "best fit" and found that I could get very close to all the numbers if I pushed in the following

 

H 1.941387218

K 4.366854884

N 5.817678593

C 5.877435799

O 7.340505544

M 7.603136588

W 8.709634012

S 8.966204991

E 9.058950648

F 10.13546858

R 10.59238625

Z 13.27188824

U 16.8611718

P 17.38422521

D 18.16935517

G 19.33591223

A 20.44785112

T 21.50164429

B 23.57054932

L 23.64017927

I 24.61005161

V 26.81398993

 

Putting these in order I note that H, K, N, C and O are elements close to the top of the periodic table. I note that N and C have very close values. Is Chemistry a clue?

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K is potassium (Kalium)

 

I remember my great aunt used to drink Kali Water, it tasted awful, just salty really. You will be more familiar with Soda Water.

 

I am just looking for a why to assign values to letters, I could for example chose the first element with that letter in its symbol, then take the value of some property, add them up and round to the nearest integer.

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Hi gnpatterson,

I recall I got non-integer values also. It would be nice if they were integers (damn it!)!

 

Makes me wonder if a "c" in Curie is not equal to a "c" in Planck... that would be devious.... In other words, maybe there is a function that needs to be employed from one name to the next. I don't know. This puzzle pisses me off. :)

 

Thanks to everyone taking a stab at this one. I'm dying to know the relation.

 

Cheers,

w=f[z]

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even so, K is either 19 or 39 (depending on what you look at).

Certainly not 4.

 

the only "4" that I can see is that it`s the 1`st element in Period 4.

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Well, if it helps, I think I see a pattern with the lower number values. Most of them have "r"s, so may that be a clue? Some may have lower letter counts, but the fact that most lower value names have the letter "r" can't be a coincidence... That could be a start. Just finding patterns in the values and letters... That's something a computer might not be able to do well.

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I am very frustrated with this problem.

 

The problem has to be one that responds to "intelligence" (what ever that might be) but the information given is over-constrained and possibly has errors in it.

 

I used a systematic method of producing a function from the square of the differences of the values I calculate (guess) and those given;

 

I ask the computer to minimise this value;

 

If I use lippman the closest I can get is a value of about 6

 

If I use lippmann I get closer ie 2.15 from this I conclude the given spelling of lippman is not the one used to calculate the value given

 

OR as usual I am being too clever and havent got the right methodology

 

I feel that previous questions have submitted not my intelligence but to my education and to solve the problems like the furbles I have to get educated in the appropriate areas.

 

Since this problem claims to be a sort of replacement cypher with linear algebra I should have the right tools already, they just don't seem to work, what am I doing wrong?

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You can think about attacking the problem from the other end and look for a pangram that encodes the information.

 

If you think about it you must at some point have to fill in for jxyq or at the very least you have to fill in for y so the solution must in some way make the choice of y obvious. You cant simply have four blanks in the mapping that you have to guess.

 

The way I might do it is to use a pangram or a close to pangramatic sentence for example

 

The quick brown fox jumps over the lazy dog - this is the classic

 

next you remove the duplicates either from the back or the front, here I'll take them from the back

 

t h e q u i c k b r o w n f x j m p s v r l z y d g

1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526

 

now you have a cypher that if you know most of it you can fill in the gaps with some intelligence

 

now of course you can make it harder, write it backwards, interleave the sequence or something like that but at the core you have to have a recognisable pangram (or holoalphabetic sentence).

 

Using a stocastic process I get a range of sequences

 

HWKNCOFSREMZUGPALDTIBV

 

or

 

HKNFCMDEROSZWUPGTBALVI

 

or

 

WHKNOSCFREMZUGPALITDBV

 

the last one looks a bit like "Why know ..." but I don't know the rest, this is probably a red herring anyway

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Now I'm looking for a unique set of the numbers 1 to 26 based on the 26 physicists given. For example the day of the DOB of each one or something like that.

 

The set up of the puzzle has to be based on some reason. perhaps the clue is in the phyicists them selves. I know that they are listed in the order that they got their nobles so I don't thing this is going to be used as a key. In some way they might give the key values in some standard fact about them.

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I am very frustrated with this problem.

...

Since this problem claims to be a sort of replacement cypher with linear algebra I should have the right tools already, they just don't seem to work, what am I doing wrong?

 

I know the feeling gnpatt. Since you are spending a lot of effort on this, it might be worthwhile to read the other forum thread (provided in the original post) if you haven't already.

 

I'd like to punch the originator of this puzzle in the face. :)

 

If this has a solution though, we're likely to stumble on it sooner or later. Sorry, but lately I just can't spare the time to attack it myself (but I've already spent a lot of time on it...). :)

 

Thanks for your efforts though!

Cheers,

w=f[z]

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is it significant that the names are presented as 2 banks of 13?

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Wait... 2 of 13?

That's 26... Number of letters in the alphabet... Perhaps the first letters in their names are a clue?

 

EDIT: Sorry 'bout this, but I just checked about the first letters, and that's a big NO. It was a good guess, but that did nothing. I guess having 26 though has something to do with solving it...

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