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Math Help - Help getting into a puzzle

  1. #1
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    Jul 2011
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    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.
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  2. #2
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    Joined
    Jul 2011
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    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.
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  3. #3
    MHF Contributor
    Opalg's Avatar
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    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.
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  4. #4
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    Jul 2011
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    Thumbs up 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
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