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

Home > Just Math
Product equals sum (Posted on 2016-01-17) Difficulty: 4 of 5
Let's start with an easy problem : What three positive integers have a sum equal to their product?
answer: (1,2,3), of course.

This puzzle can easily be transformed into a D4 problem:

For what values of k will the question "What k positive integers have a sum equal to their product?" have only one unique set of integers for an answer?
Clearly for k=2 the answer is unique: (2,2) and so it is for k=4: (1,1,2,4).

List all other values of k below 1000.

No Solution Yet Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
some solutions | Comment 1 of 6
Without computer assistance, finding all possible values for K below 1000 is not worth doing. As I don't plan of using a computer to iterate through all possible solutions, I only list a solution for each K from 5 to 14 [k={2,3,4} has already been given in the problem]. To demonstrate that a given K might have more than one solution, I provide one for K=14.
 K
 5 (1,1,2,2,2) :=8
 6 (1,1,1,1,2,6) :=12
 7 (1,1,1,1,1,3,4) :=12
 8 (1,1,1,1,1,2,2,3) :=12
 9 (1,1,1,1,1,1,1,2,9) :=18
10 (1,1,1,1,1,1,1,1,4,4) :=16
11 (1,1,1,1,1,1,1,1,2,2,4) :=16
12 (1,1,1,1,1,1,1,1,1,1,2,12) :=24
13 (1,1,1,1,1,1,1,1,1,1,1,3,7) :=21
14 (1,1,1,1,1,1,1,1,1,1,1,2,2,5) :=20
14 (1,1,1,1,1,1,1,1,1,1,1,1,2,14) :=28

  Posted by Dej Mar on 2016-01-17 11:04:37
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