perplexus.info :: Numbers : Arithmetic Sequence Crossed Integer Triplet Puzzle

Arithmetic Sequence Crossed Integer Triplet Puzzle (Posted on 2022-09-21)

Determine all possible triplets (a,b,c) of positive integers, with a>b>c, such that:

a+bc < b+ca < c+ab are three expressions in arithmetic sequence, and:
a+b-c=22

Submitted by K Sengupta

Rating: 5.0000 (2 votes)

Solution: (Hide)

(a,b,c) = (19,10,7), (19,13,10) are the only possible triplets that satisfy the given conditions.
For an explanation, refer to:
The analytical solution submitted by: broll in this location.
The computer program assisted solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: another take; same answer	K Sengupta	2024-02-01 11:43:42
re: Possible Solution	K Sengupta	2024-02-01 11:42:32
Possible Solution	broll	2022-09-22 00:09:17
No negative solutions	Steve Herman	2022-09-21 11:06:45
another take; same answer	Charlie	2022-09-21 09:29:29
computer solution	Larry	2022-09-21 08:10:09

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 (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info