you have the numbers from 1 through 9. divide them into 3 groups so that each group has the same total after adding the digits in them..
i got until: adding all the digits makes 45 and and divided by 3 so each will be 15, but what next? any method for that or do it by trial and error?
how about this one:
8 1 6
3 5 7
4 9 2
Each row, each column and each diagonal adds up to 15
Thanks a million!! but how did you get to it? is there a formula or method to deal with this kind of questions or just try to switch around and maybe stumble upon the right one? actually i was working on it, too and came up with 8 7, 9 6, 1 2 3 4 5 ,(as it did not say the groups has to have the same amount of numbers in them, only that the total has to be the same..)
your answer is very elegant
yes, there are methods and "formulas" to do these
Google "magic squares" and you will see all kinds of stuff
There is a very easy pattern for any odd-sized square which should be found in the first few results
Even-sized squares are a bit more difficult
To divide the numbers from 1 through 9 into 3 groups such that each group has the same total after adding the digits, you can follow a method instead of relying on trial and error.
First, let's calculate the total sum of all the digits from 1 to 9:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
Since you correctly noted that this sum divided by 3 will be 15, our goal is to assign each number to one of the three groups so that the sum of the digits in each group is 15.
Here's a step-by-step process to achieve this:
1. Start by creating three empty groups: Group A, Group B, and Group C.
2. Pick any number from 1 to 9 and place it in Group A.
3. Now, calculate the difference between 15 and the number you just placed in Group A. Let's call this difference "X."
4. Look for a number in the remaining set of numbers whose sum of digits is equal to X.
5. Place this number in Group B.
6. Calculate the difference between 15 and the sum of digits in Group B and find a number from the remaining set to equal this difference.
7. Place this number in Group C.
8. Repeat steps 6 and 7 for the remaining numbers until you have assigned all the numbers to the three groups.
Keep in mind that the difference you calculate in each step must match the sum of digits of one of the remaining numbers. If you get to a point where no number fits the difference, or if you cannot complete the process, then it may indicate that there is no solution for dividing the numbers with equal digit sum in three groups.
By following this systematic approach, you can divide the numbers 1 through 9 into three groups with the same total after adding the digits.