Very hard Maths problem

[Ste]

Ok, I can't do it I spent a good 2 hours on it last night and I got nowhere.

So I'm offering it up to you lot:

Each letter of the alphabet has been assigned a different value (from 1 to 26), no letter having the same value as that of it's position in the alphabet (eg A hasn't a value of 1, z hasn't a value of 26 etc). All of the values remain the same throughout the puzzle. What is each letter's value?

1. B/X = E - (V + R)

2. C + K = T

3. Z * P = L

4. F + Y = Q

5. C * Y = O

6. M + H = T

7. T + T = I

8. L/H = C

9. G + J = T

10. T - V = D - (A + R)

11. P + R + K = Z

12. S - A = J + P

13. U > N

14. I - R = W

15. M * J = D

someone must be able to at least have a go at this.
Let me know how you get on.

[EDIT] If you want to challenge yourself don't read the replies as the answer is there, have a go first! [/EDIT]

[Mushroom]

toaster.

[acropolis]

hey shouldn't your answer be an 11-dimensional 'space' of infinite extent in all directions?

cuz you've got 15 equations for 26 variables. that's not very many!

[queball]

Originally posted by acropolis
hey shouldn't your answer be an 11-dimensional 'space' of infinite extent in all directions?

cuz you've got 15 equations for 26 variables. that's not very many!

No, because you know they are all integers 1-26 and that they are all different. That's only a finite space.

[acropolis]

Originally posted by queball
No, because you know they are all integers 1-26 and that they are all different. That's only a finite space.

26! (exclamation mark not used as punctuation here)

good point! (exclamation mark used as punctuation here)

L = 18,20, or 24...

P = 2

[Muslim]

i do law, i know nothing about numbers,
i used to, nut now i dont.... its sad when you realize you keep getting stupider with each year that goes by /o\

[Ragnarak]

seen this (or something virtually the same) on here before, think quite a few ppl managed to get it done

[Anu]

sounds like fun

[W]

Originally posted by acropolis
26! (exclamation mark not used as punctuation here)

good point! (exclamation mark used as punctuation here)

L = 18,20, or 24...

P = 2

I tried to let my comp search for a solution with p=3 and l=18 (and other derived limits), but it's still too big a space, couldn't disprove it by exhaustion. Prove that p=2!

[Edit] My current proven matrix, add to it if you got some more:

n |abcdefghijklmnopqrstuvwxyz
--+--------------------------
1 |xxxxx  xxx xx xxx xxx   xx
2 | x xx   x  x  x x xx     x
3 |  xxx   x  x  x   xx     x
4 |   xx   x  x  xx  xx     x
5 |   xx   x  x  xx  xx     x
6 |     x  x  x   x   x     x
7 |   x  x x  x  xx          
8 |       xx  x   x          
9 |        x  x   x          
10|        xx x   x          
11|   x    x xx  xx x        
12|        x xx   x x        
13|  xx  xxxxxxx xx x        
14|  x   xx xx xx x x     xxx
15|  x   xxxxxxx xx x     xxx
16|  x   xx xx x  x x     xxx
17|  xx  xxxxxxx xxxx     xxx
18|  x   xx xx x  x x     xxx
19|  xx  xxxxxxx xx xx    xxx
20|  x   xx xx x  x x x   xxx
21|  x   xxxxxxx  x x  x  xxx
22|  x   xx xx x  x x   x xxx
23|  xx  xxxxxxx xx x    xxxx
24|  x   xx xx x  x x     xxx
25|  x   xxxxxxx  x x     xxx
26|x x   xx xx xx x x x xxxxx
--+--------------------------
   abcdefghijklmnopqrstuvwxyz

[queball]

I=T+T so I<=26 => T<=13

n |abcdefghijklmnopqrstuvwxyz
--+--------------------------
1 |xxxxx  xxx xx xxx xxx   xx
2 | x xx   x  x  x x xx     x
3 |  xxx   x  x  x   xx     x
4 |   xx   x  x  xx  xx     x
5 |   xx   x  x  xx  xx     x
6 |     x  x  x   x   x     x
7 |   x  x x  x  xx
8 |       xx  x   x
9 |        x  x   x
10|        xx x   x
11|   x    x xx  xx x
12|      xxx xxx  x x
13|  xx  xxxxxxx xx x
14|  x   xx xx xx x x x   xxx
15|  x   xxxxxxx xx x x   xxx
16|  x   xx xx x  x x x   xxx
17|  xx  xxxxxxx xxxx x   xxx
18|  x   xx xx x  x x x   xxx
19|  xx  xxxxxxx xx xxx   xxx
20|  x   xx xx x  x x x   xxx
21|  x   xxxxxxx  x x xx  xxx
22|  x   xx xx x  x x x x xxx
23|  xx  xxxxxxx xx x x  xxxx
24|  x   xx xx x  x x x   xxx
25|  x   xxxxxxx  x x x   xxx
26|x x   xx xx xx x x x xxxxx
--+--------------------------
   abcdefghijklmnopqrstuvwxyz

edit: drew this wrong

[Anu]

:(
Found 16 letters manually. Should be done soon, hopefully

[queball]

And like acropolis said, L must be able to be factorised two ways. So 12, 18, 20, 24 are ok, but if L=12 then C,H,P,Z are 2,3,4,6 in some permutation, and Z-P=R+K which is impossible.


edit: Z-P not P-Z, not that it's important

[Bloomers III]

but what does it all mean basil?

[W]

Originally posted by queball
T<=13

Forgot to add that one, thx.

Originally posted by Anu
:(
Found 16 letters manually. Should be done soon, hopefully

You know, I have this equation, a+b=c+d, where all the numbers are positive integers. I know a=2, b=3 and c=8, but I haven't been able to find d yett. Only a matter of time tho!

[Anu]

P=2 L=20 K=7 R=1 H=5 C=4 Z=10 T=11 I=22 W=21 M=6 Y=5 O=12 J=3 D=18 G=8

or

P=2 L=24 K=9 R=1 H=6 C=4 Z=12 T=13 I=26 W=25 M=7 Y=5 O=20 J=3 D=21 G=10

Is what i've found. the rest should be 'easy'. But I'm getting rather tired

edit: Fixed typos

[Anu]

the second one is the right one.

Last letters:

A=18 S=23 V=11 B=15 X=3 E=17 F=8 Q=14 U=22 N=16

[queball]

How many 3's do you need?

[Anu]

the last one is correct as stated

but for you, i'll edit the first one, which was originally wrong

edit: fk.

[Ragnarak]

Originally posted by Anu
the last one is correct as stated

but for you, i'll edit the first one, which was originally wrong

j=3 and x=3?

[Anu]

A=18 B=16 C=4 D=21 E=14 F=17 G=10 H=6 I=26 J=3 K=9 L=24 M=7 N=15 O=20 P=2 Q=22 R=1 S=23 T=13 U=19 V=11 W=25 X=8 Y=5 Z=12

Hopefully right this time :(

[queball]

[Ste]

damnit so it is possible.

*sigh* I'll just have to get a bigger sheet of paper.
don't have my calculations with me at the moment but will have another go when I'm home and bored tonight.

How long did it take you?

[Anu]

About 3 hours efficiently.

Hint: start with these formulas;

Z*P = L
P+R+K = Z

L/H = C
C+K = T and the fact that T = {9,10,11,12,13}

[acropolis]

Originally posted by Anu
About 3 hours efficiently.

Hint: start with these formulas;

Z*P = L
P+R+K = Z

L/H = C
C+K = T and the fact that T = {9,10,11,12,13}

that was the corner i started working on.

i got pissy after a while because too many of the variables only showed up in one equation, so there was nothing to do but guess and check.

Originally posted by Anu
A=18 B=16 C=4 D=21 E=14 F=17 G=10 H=6 I=26 J=3 K=9 L=24 M=7 N=15 O=20 P=2 Q=22 R=1 S=23 T=13 U=19 V=11 W=25 X=8 Y=5 Z=12

Hopefully right this time :(

fking wait a second that's basically what i had when i thought i hit a contradiction! i'm gonna be pissed if it turns i just did stupid...

[Anu]

C*Y=O helps you elminate quite a few possibilities

[acropolis]

****! I'm now looking back at my notes from yesterday.

I had
c = 4
d = 21
g = 10
h = 6
i = 26
j = 3
k = 9
l = 24
m = 7
o = 20
p = 2
r = 1
t = 13
w = 25
y = 5
z = 12

and then i solved (10) to
13 - V = 20 - A
which on the next line of my notes became
A - V = 13.

You should be unsurprised that I soon found a contradiction, and didn't feel like starting over.

I declare myself "Official GD Idiot" for to-day