 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Threes and sevens (Posted on 2006-10-25) You can decide whether a number is divisible by 3 by forming its cross sum, that is the sum of all its decimal digits: It is divisible by three exactly if its cross sum is. Similarly, a three-digit number is divisible by seven if (and only if) the sum of twice its most significant digit plus three times its middle digit plus its least significant digit is divisible by seven.

Can you find a similar scheme for checking divisibility by 33 and 37, for numbers with an arbitrary number of digits?

 No Solution Yet Submitted by vswitchs Rating: 2.5000 (2 votes) Comments: ( Back to comment list | You must be logged in to post comments.) Another answer for 37 | Comment 5 of 7 | With the digits being a_0, a_1,... take the following "cross-sum"

a_0 + 10a_1 - 11a_2 +a_3+10a_4-11a_5+...

It can be nicely calculated because no multiplication is required; the "11a_i"-term is simply given by concatenating the digit a_i with itself.

Example:

13140452172 -> 72-11+52-44+40-11+13=111 -> 11-11=0 => divisible by 37

 Posted by JLo on 2006-10-25 12:19:36 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 (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2019 by Animus Pactum Consulting. All rights reserved. Privacy Information