New Scientist Enigma Number 505 – A Pretty Puzzle
by Christophe Maslanka
From Issue #1657, 25th March 1989
I was just sitting down to crumpets and honey in The Wykeham Tea Room when Bob Cowley appeared carrying a basketball. He handed me a slip of paper. “A, B & C all stand consistently for digits throughout this equation. I won’t tell you whether any of the digits are the same or not as l don’t want to spoil your fun,” said Bob.
Certainly, it was a pretty equation:
(BAABC x BA) – BAABC = ABCABC
though l had once seen a prettier one in an amusement arcade in Bognor Regis. It should, of course, be as easy as ABC to solve this before the crumpets cool. Can you help me by sending me the digits corresponding to A, B and C?
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Brian Gladman permalink123456789101112131415# The equation can be re-arranged to allow C to be# computed from A and B:## ABC = 1000.BA.(BA - 1) / (1002 - BA)for BA in range(11, 100):ABC, r = divmod(1000 * BA * (BA - 1), 1002 - BA)if not r:B, A = divmod(BA, 10)AB, C = divmod(ABC, 10)if AB == 10 * A + B:s = f"{BA}{ABC}"print(f"A = {A}, B = {B}, C = {C} [ ({s} x {BA}) - {s} = {ABC}{ABC} ]")
