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Sum, difference and equality puzzle

  1. Feb 4, 2010 #1
    Substitute each of the capital letters by a different digit from 0 to 9 to satisfy this set of cryptarithmetic relationships. None of the numbers can contain any leading zero.

    GEORGE + RUGGLE + 15750 + 16220 + P = PPPPPP, and:

    OE - LR = LO, and:

    RUGGLE is divisible by 7
     
  2. jcsd
  3. Jun 10, 2010 #2
    E=0 I think
     
  4. Feb 27, 2011 #3

    I like Serena

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    Since E + E + P -> P, E must be either 0 or 5, so E is a multiple of 5.

    RUGGLE is a multiple of 7 and a multiple of 5, so ruggle is a multiple of 35.

    With RUGGLE being 6 digits and R nonzero, that means that the lowest value for RUGGLE is 123375 and the highest 987735.

    With OE - LR = LO it follows that O = (20 x L + R - E) / 9

    Looking at the 5th digit of the sum it follows that:
    P = (G + L + 5 + 2 + 2 x E / 10) mod 10

    Now we can simply enumerate all possible values of RUGGLE, calculate O and P and check if the conditions are met.
    Finally only 1 answer remains.

    george + ruggle + 15750 + 16220 + p = pppppp oe - lr = lo
    609160 + 136640 + ..... + ..... + 7 = 777777 90 - 41 = 49
     
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