Row total and column total puzzle

In summary, a row total and column total puzzle is a mathematical puzzle where a grid of numbers is given and the goal is to fill in the missing numbers so that each row and column add up to a specific target number. The purpose of this puzzle is to exercise logical thinking and problem-solving skills, as well as improve mathematical abilities. To solve the puzzle, one can use strategies such as looking for patterns, using target numbers to eliminate possibilities, and starting with rows or columns that have fewer missing numbers. There are also various variations of this puzzle, including different operations, grid sizes, target numbers, and additional constraints.
  • #1
K Sengupta
113
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.
 
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  • #2
Code:
[color="lightblue"]6 9 8
5 7 1 
4 3 2[/color]
 
  • #3
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
 

What is a row total and column total puzzle?

A row total and column total puzzle is a type of mathematical puzzle where a grid of numbers is given, and the goal is to fill in the missing numbers in a way that each row and column add up to a specific target number.

What is the purpose of a row total and column total puzzle?

The purpose of a row total and column total puzzle is to exercise logical thinking and problem-solving skills. It can also help improve mathematical skills, such as addition and subtraction.

How do you solve a row total and column total puzzle?

To solve a row total and column total puzzle, start by looking for any numbers that have a limited number of possible combinations. Then, use the given target numbers to narrow down the possibilities for the remaining empty spaces until the puzzle is complete.

Are there any strategies for solving a row total and column total puzzle?

Yes, there are a few strategies that can help with solving a row total and column total puzzle. These include looking for patterns in the given numbers, using the target numbers to eliminate possibilities, and starting with the rows or columns that have the fewest missing numbers.

Are there any variations of the row total and column total puzzle?

Yes, there are several variations of the row total and column total puzzle. Some may involve different operations, such as multiplication or division, and others may have different grid sizes or target numbers. Some puzzles may also have additional constraints, such as only using odd or even numbers.

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