# Math Help - Help getting into a puzzle

1. ## Help getting into a puzzle

Firstly, I'm asking this to solve a puzzle at Geocaching.com - have a look. It isn't for homework, but I thought some of you may be interested in it anyway.

Each letter A to Z represents a number from 1 to 26 - all you need to do is work out which number corresponds to which letter. The value for the letter Z can be determined by elimination.

A + B = D
B * K = C
F * U = D
F * K = L
H + I = J
Q * Q = R
R + S = T
T = K * G
U + V = W
F + K = Q
W + H = O
D + E = N + P
V * W = X + Y
O + V = N
M + I = Y
Any hints or tips in getting this sorted will be greatly appreciated.

2. ## Re: Help getting into a puzzle

A + B = D
B * K = C
F * U = D
F * K = L
H + I = J
Q * Q = R
R + S = T
K * G = T
U + V = W
F + K = Q
W + H = O
D + E = N + P
V * W = X + Y
O + V = N
M + I = Y

Just swapped equation 8 around to fit the format of the others.

3. ## Re: Help getting into a puzzle

I don't want to do the puzzle for you, but here are a few hints to get you started. I'll number the equations for reference.

(1) A + B = D
(2) B * K = C
(3) F * U = D
(4) F * K = L
(5) H + I = J
(6) Q * Q = R
(7) R + S = T
(8) K * G = T
(9) U + V = W
(10) F + K = Q
(11) W + H = O
(12) D + E = N + P
(13) V * W = X + Y
(14) O + V = N
(15) M + I = Y

The best equation to use as a starting point is (6), which tells you that R is the square of Q, and so Q cannot be greater than 5 (remember that none of the numbers can be greater than 26). But from (4) each of the numbers F and K is greater than 1. Hence from (10) Q is at least 5. Therefore Q=5 and R=25. Also, F and K must be 2 and 3 (but we don't yet know which is which). From (4), L=6.

Thus the values 2,3,5 and 6 are taken, and the smallest remaining values are 1, 4, 7, ... . Next, look at V. If V=1 then (13) would tell you that W = X+Y. Use (15), (9) and (3) to see that that would make D impossibly large. Therefore V cannot be equal to 1.

Use similar techniques to show that it is also impossible for V to be 7 or greater. Therefore V must be equal to 4.

I haven't tried to go beyond that, but I guess the next useful thing might be to find out which letter represents 1.

4. ## Re: Help getting into a puzzle: Solution

I have now solved this puzzle, thanks to the starting points given here. Thank you very much.

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