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

Home > Numbers
Six sets (Posted on 2014-02-17) Difficulty: 3 of 5
Please scrutinize the following sets of integers:

S1 (2, 5, 8)
S2 (22, 55, 888, 201)
S3 (232, 88781, 20)
S4 (1, 635, 5, 868, 781, 20 ,115)
S5 (26, 3 ,19, 110, 35, 544, 82, 68, 781, 207)
S6 (3 ,14, 15, 926, 535)


I am choosing one random member from each set :
e.g. 2, 888, 20, 1, 544 and 926.

Sum of those numbers apparently ends by 1.

How many distinct results generated this way will terminate by 1?

How many by a zero digit?

Any comments?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Ignoring distinct p&p but it has an error | Comment 4 of 7 |
If I didn't worry about the sums being distinct I only had to worry about the last digit.  This made a p&p straightforward for me.
There are 3*4*3*7*9*5=11340 ways of choosing a number from each set.
I essentially made a tree-diagram with overlapping branches.  And went in order of sets 5,4,6,2,1,3 to get the larger sets out of the way first.
Results:
1131 end in 0
1137 end in 1
1136 end in 2
1132 end in 3
1132 end in 4
1135 end in 5
1135 end in 6
1133 end in 7
1136 end in 8
1133 end in 9

As for Ady's comment.  I don't see much in S5 except I JUST NOTICED I MADE A BIG MISTAKE.  I MISSED THE 19.  EVERY DIGIT IS IN THAT SET AND I COULD HAVE COMPLETELY IGNORED IT. To do it my way anyway.

There's no obvious reason to ignore S5 if you're looking for 'distinct' sums.  Although 1260 is the product of the other set sizes.

S6 is a parsing of pi.


  Posted by Jer on 2014-02-18 00:11:36
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 (2)
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