Write the numbers1, 2, 3, 10, 11, 12, 19, 20 and 21 into the fields of a 3x3 grid so that the sum of the numbers in each row, column and diagonal is the same.
PLZ HELP DUE TOMORROW!
I need to know, which order to put those numbers on a 3x3 grid, so I get the same answer for each number! ( I'm confused too ) ( Canada, Toronto )
The sum of all the numbers is 99, so each row must sum to 33
10+11+12 = 33, so maybe that will form a diagonal. A little playing around, placing 19,20,21 in different rows and columns, gave me
19 3 11
2 10 21
12 20 1
Thanks for helping my son again, the teacher goes very strict on him :)
To solve this puzzle, you need to find a way to arrange the given numbers in a 3x3 grid such that the sum of the numbers in each row, column, and diagonal is the same. Here's a step-by-step guide to help you find the solution:
1. Start by listing down all the given numbers: 1, 2, 3, 10, 11, 12, 19, 20, and 21.
2. Since the sum of each row, column, and diagonal should be the same, let's represent this sum as "S."
3. Begin filling in the grid by placing the largest number, 21, at the center of the grid. This is because the central number belongs to both diagonals and will help balance their sums.
4. Now, let's consider the possible positions for number 21:
- Placing 21 in the middle row would require the sum of the other two numbers in that row to be S - 21, which means both numbers should be less than or equal to 21. However, the only available numbers for that row are 19 and 20, and their sum exceeds 21. So, this option is not possible.
- Placing 21 in the middle column would also require the sum of the other two numbers in that column to be S - 21, which means both numbers should be less than or equal to 21. However, the only available numbers for that column are 10 and 12, and their sum is less than 21. So, this option is not possible.
- Placing 21 in either of the two diagonals would require the sum of the other two numbers in the diagonal to be S - 21, which means both numbers should be less than or equal to 21. However, the only available numbers for that diagonal are 2 and 19, and their sum exceeds 21. So, this option is not possible.
- Placing 21 in any corner of the grid (top left, top right, bottom left, or bottom right) would require the sum of the other two number in that corner's row, column, and diagonal to be S - 21. This gives us the possibility of finding suitable numbers for the remaining positions.
5. Now, let's consider the different options for placing number 21 in each corner and work through the possibilities:
a) Placing 21 in the top left corner:
- The top left corner is part of the top row, left column, and left diagonal.
- In the top row, number 21 is already present, so we need to find two numbers whose sum is S - 21.
- In the left column, number 21 is already present, so we need to find two numbers whose sum is S - 21.
- In the left diagonal, we only have one empty spot remaining, so the number in that spot should be S - 21.
- Note that the remaining numbers available are 1, 2, 3, 10, 11, 12, and 19.
- Begin by placing number 21 in the top left corner (first row, first column) of the grid.
- Now, consider the sum S - 21 and see if there are any possible combinations among the remaining numbers that yield this sum.
- Continue trying different combinations until you find one that works for both the top row and left column.
- Finally, place the remaining number in the empty spot of the left diagonal.
6. Once you have successfully placed number 21 in the top left corner, repeat the process for the remaining three corners (top right, bottom left, and bottom right).
By following this step-by-step process, you should be able to find the solution to the puzzle. Good luck!