Tell and deal puzzle

  • Thread starter K Sengupta
  • Start date
  • #1
111
0
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.
 

Answers and Replies

  • #2
668
3
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

DaveE
 

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