Answer for John Gowland's puzzle: A=44 B=72 C=837 D=175 E=64 F=49 a=48 b=777 c=28 d=314 e=46 f=59 --Marcis 4472 8378 4175 6449 --David Wilson Hi Ed, A really nice puzzle from John and one which just requires a wee bit of thought to reduce the possibilities. Realising that the terminal digit of P_Q_R is the same as the terminal digit of the cube sum helps enormously. Tabulating these reveals for instance that if P ends in a 6 and Q in a 2 then R must end in 2 or 7. Using this information along with the fact that B and E are multiples of 4 cracks the puzzle. I only used my old Casio graphics calculator to do this. No computer required!! The solution is 4472 8378 4175 6449 Cheers, Alastair Cuthbertson in sunny St. Andrews!! ------------------------------------------------------------ Linear Cubes: 4472 8378 4175 6449 Not the best form of presenting these: (16,50,33) (22,18,59) (44,46,64) (48,72,15) (98,28,27) (98,32,21) Juha Saukkola ---------------------------------------------------------- 4472 8378 4175 6449 Stephen Kloder ---------------------------------------------------------- 4472 8378 4175 6449 Jeff Smith -------------------------------------------------------- the only solutions to P^3 + Q^3 + R^3 = P_Q_R for two digit P,Q,R are P Q R 16 50 33 22 18 59 34 10 67 44 46 64 48 72 15 98 28 27 98 32 21 Realizing Q shares its second digit with R's first digit from the positioning of e and E and the first row in the table, and that A/2 must yield another P from the table, P,Q,R must be 44,46,64 From here, i completed the puzzle through algebraic computation from the table and the use of the solution set listed above. Crossnumber: 4472 8378 4175 6449 Table: P, Q, R 44,46,64 22,18,59 48,72,15 16,50,33 98,28,27 98,32,21 Regards, -David Perryman ---------------------------------------------------- Ed, I've recently discovered the wonders of Perl. Pretty fun language. My first program in it helped me solve John Gowland's "Linear Cubes" problem. Here's the answer: 4472 8378 4175 6449 Clint Weaver -------------------------------------------------