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Tell and deal puzzle

  1. Apr 1, 2009 #1
    p, q and r are three positive integers satisfying p< q< r, such that q is the arithmetic mean of p and r.

    Determine all possible triplet(s) (p, q, r) that satisfy both the cryptarithmetic equations, where each of the capital letters denotes a different decimal digit from 0 to 9 and, none of T and D can be zero.

    r4 – q4 = TELL, and:
    q4 – p4 = DEAL.
  2. jcsd
  3. Apr 1, 2009 #2
    I'm not sure if it qualifies as brute force or not-- there were only 19 different things I had to try:

    I knew that 5 <= p < 15, so I started assuming that p=5, and worked up from there. Highest you can get with a 4 digit difference was p=12, which turned out to have the only answer:

    12,13,14, TELL = 9855, DEAL = 7825

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