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

Home > Probability
Hill Numbers Settlement II (Posted on 2011-03-09) Difficulty: 3 of 5
A 7-digit base ten positive integer of the form ABCDEFG is called a modified hill number if the digits B, D and F satisfies: B = A + C (mod 10) , D = C + E (mod 10) and F= E + G (mod 10) (Each of the capital letters in bold denotes a digit from 0 to 9, whether same or different.)

Determine the probability that x is a modified hill number, given that x is a base ten positive integer chosen at random between 1000000 and 9999999 inclusively.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 2 of 5 |

The numbers are determined by A, C, E and G, and any digits can be used in these four positions except that A cannot be zero in the range given.

There are 9 choices for A and 10 each for C, E and G, for a total of 9000 possibilities out of the 9999999 - 999999 = 9,000,000.

The probability is 9,000 / 9,000,000 = 1/1000.

Done this way it seems like a D2.


Another way of figuring it:

B has 1 chance in 10 of satisfying the condition, as does D, and the same for F. Multiplied together that's 1/1000.

Now it seems like a D1.


  Posted by Charlie on 2011-03-09 15:10:32
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 (5)
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