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

Home > Just Math
Near Pandigital Ponder (Posted on 2014-11-26) Difficulty: 3 of 5
Base ten positive integers P, Q, R, S and T together uses the base ten digits 1, 3, 5, 6, 7 and 9 precisely twice.

What are the respective minimum and maximum values of P*Q*R*S*T?

*** None of P,Q,R, S can contain the digits 0,2,4,6,8.

No Solution Yet Submitted by K Sengupta    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution An Algorithm Comment 1 of 1
I started by figuring out the possible lengths of five numbers using twelve digits.  I got the following twelve distributions: 8-1-1-1-1, 7-2-1-1-1, 6-3-1-1-1, 6-2-2-1-1, 5-4-1-1-1, 5-3-2-1-1, 5-2-2-2-1, 4-4-2-1-1, 4-3-3-1-1, 4-3-2-2-1, 4-2-2-2-2, 3-3-2-2-2.

For each distribution I created a template of the numbers left-aligned, for example the 6-2-2-1-1 template is:
XXXXXX
XX
XX
X
X

To find the minimum product start with the leftmost column and place the five smallest digits available in descending order.  Repeat for each column working to the right.  For the 6-2-2-1-1 template this yielded:
567799
36
35
1
1
This product is 715,426,740, which is the smallest for the 6-2-2-1-1 template.

Over all 12 templates the absolute smallest occurred for the 8-1-1-1-1 template yielding:
55667799
3
3
1
1
This product is 501,010,191.  This set of numbers satisfies the constraint that implies both 6s are in the same number.

To find the largest product the same templates are used but taking the largest available digits each time, with the first column in ascending order and the other columns in descending order.  The absolute maximum product occurs with the 3-3-2-2-2 template:
661
751
75
93
93
This product is 322,009,405,425.  Again, this set of numbers satisfies the constraint that implies both 6s are in the same number.

  Posted by Brian Smith on 2017-10-25 13:23:04
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 (3)
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