Row total and column total puzzle

  • Context: Undergrad 
  • Thread starter Thread starter K Sengupta
  • Start date Start date
  • Tags Tags
    Column Puzzle Row
Click For Summary
SUMMARY

The discussion revolves around solving a 3x3 grid puzzle using the digits 1 to 9, where each digit appears exactly once. The column totals are specified as 15, 19, and 11, while the row totals are 23, 13, and 9. The solution provided is as follows: the first row contains 6, 9, and 8; the second row contains 5, 7, and 1; and the third row contains 4, 3, and 2. This arrangement satisfies all the given conditions for both rows and columns.

PREREQUISITES
  • Understanding of basic arithmetic operations
  • Familiarity with combinatorial puzzles
  • Knowledge of the properties of magic squares
  • Ability to manipulate and analyze numerical data
NEXT STEPS
  • Explore techniques for solving combinatorial puzzles
  • Learn about the properties and variations of magic squares
  • Investigate strategies for optimizing grid-based problem-solving
  • Study algorithms for generating permutations of a set of numbers
USEFUL FOR

Puzzle enthusiasts, educators in mathematics, and anyone interested in combinatorial problem-solving techniques will benefit from this discussion.

K Sengupta
Messages
113
Reaction score
0
Arrange the nine cells of a 3x3 square with digits from 1 to 9, with each digit occurring exactly once, such that:

## The respective totals of the first column, second column and the third column are 15, 19 and 11, and:

## The respective totals of the first row, second row and the third row are 23, 13 and 9.
 
Mathematics news on Phys.org
Code:
6 9 8
5 7 1 
4 3 2[/color]
 
Found solution 1: a=6 b=9 c=8 d=4 e=7 f=2 g=5 h=3 i=1
6 9 8
4 7 2
5 3 1


Found solution 2: a=6 b=9 c=8 d=5 e=7 f=1 g=4 h=3 i=2
6 9 8
5 7 1
4 3 2


Found solution 3: a=8 b=9 c=6 d=2 e=7 f=4 g=5 h=3 i=1
8 9 6
2 7 4
5 3 1


Found solution 4: a=8 b=9 c=6 d=5 e=7 f=1 g=2 h=3 i=4
8 9 6
5 7 1
2 3 4
 

Similar threads

  • · Replies 68 ·
3
Replies
68
Views
12K
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 1 ·
Replies
1
Views
5K
  • · Replies 10 ·
Replies
10
Views
5K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 14 ·
Replies
14
Views
6K
  • · Replies 4 ·
Replies
4
Views
3K