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

Arithmetic Sequence Crossed Integer Determination Puzzle (Posted on 2023-02-12)

+----+----+----+----+
| 23 |    |    |    | 
+----+----+----+----+
|    |    | 64 |    |
+----+----+----+----+
|    |  N |    |    | 
+----+----+----+----+
|    |    |    |101 |  
+----+----+----+----+

In the 4x4 grid provided above:

Each the 16 values appearing in the 16 cells is a positive integer.
The 4 values corresponding to each of the 4 rows are in arithmetic sequence.
The 4 values corresponding to each of the 4 columns are in arithmetic sequence.

Determine the total number of distinct positive integer values that N can assume.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The total number of distinct positive integer values that N can assume is 27.
For an explanation, refer to the analytical solutions posited by Larry and Steve Herman here and here.
Charlie has also submitted a computer program assisted solution in this location.

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

Subject	Author	Date
the full grids	Charlie	2023-02-13 19:17:32
Counting analytically	Steve Herman	2023-02-12 19:30:05
re: Solution with correction	Larry	2023-02-12 15:56:05
re: computer solution	Charlie	2023-02-12 09:38:58
computer solution	Charlie	2023-02-12 09:16:29
Solution	Larry	2023-02-12 08:07:54

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (1)
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