All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
How and When (Posted on 2009-07-29) Difficulty: 2 of 5
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)

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Integrity? (interesting property) | Comment 3 of 17 |
(In reply to re: Integrity? (interesting property) by Daniel)

Hey, Daniel!  We seem to have radically different understandings of this problem.  By "integrity" I was just pointing out that the cube roots of the three terms were NOT integers (my first go at the problem was to see if there were a solution where the roots were integers, to obviate questions of the precision required for the test sum).  By substituting (x,y,z,) for (HOW,AND,WHEN) you do not seem to be approaching "this alphametic" as such. We are explicitly told that each capital letter stands for a decimal digit, so (e.g.) HOW = 100*H + 10*O+W ,u.s.w., and that the assignments to each letter must be consistent throughout (e.g. "H" is the same digit in HOW as in WHEN).

I approached it via brute force generation (seven loops, etc.), but there may be some method via factoring the three numbers.  In my solution, (192 = 3*2**6), (375 = 3*5**3) and (2187 = 3**7), though that doesn't immediately suggest to me an approach.

Perhaps the proposer (K Sengupta) can explicate.

 


  Posted by ed bottemiller on 2009-07-29 19:39:21
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (12)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information