Solve this alphametic, where each of the capital letters in bold denotes a different decimal digit from 0 to 9. None of the numbers can contain any leading zero.

³√(HOW)+ ³√(AND) = ³√(WHEN)

No smoke or computer screens needed for this check..

    192^(1/3) + 375^(1/3)
= (64 x 3)^(1/3) + (125 x 3)^(1/3)
= 64^(1/3) x 3^(1/3)    +    125^(1/3) x 3^(1/3)
= 4  x  3^(1/3)  +  5  x  3^(1/3)
= 9  x  3^(1/3)
= 729^(1/3)  x  3^(1/3)
= (729 x 3)^(1/3)
= 2187^(1/3)

 

Edited on July 31, 2009, 9:44 pm

Edited on July 31, 2009, 9:50 pm

Posted by Harry on 2009-07-31 21:40:22