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

Home > Just Math > Calculus
Edgy Integral (Posted on 2009-03-25) Difficulty: 2 of 5
Solve this alphametic integral puzzle, where each of the capital letters in bold represents a different decimal digit from 0 to 9, given that C and N are constants and, E is not zero.

B
∫ C*xN dx = EDGE
A

See The Solution Submitted by K Sengupta    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Another way Comment 4 of 4 |
Evaluating the integral, we have:

EDGE = C * [ B^(N+1) - A^(N+1)] / (N+1)

EDGE / C = [ B^(N+1) - A^(N+1)] / (N+1)

EDGE / C will have 3 or 4 digits.

A quick inspection shows that this occurs only for N =< 4.

I used a spreadsheet to obtain which follows.

The values on the rhs that end in 0, can be eliminated, and also N=4.

The possibilities to be analyzed are (calling r the value of the rhs):

(N, B, A, r) = (3, 9, 5, 1484), (3, 8, 0, 1024), (3, 7, 5, 444), (3, 6, 0, 324), (3, 5, 1, 156), (2, 9, 0, 243), (2, 9, 3, 234), (2, 9, 6, 171), (2, 8, 5, 129) and (2, 7, 1, 114).

Knowing that the r (the rhs) multiplied by C must yield EDGE, that is, the same digit at left and at right, we quickly found the unique possibility for (N, B, A): (3, 6, 0). The rest follows.

 

  Posted by pcbouhid on 2009-03-26 11:45:03
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 (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information