Magic Triangle

Directions: Arrange the numbers 1, 2, 3, 4, 5, 6 so each row has a sum of 9. Use all six numbers and each number once.


Magic triangle











Hint: What combination of three of these numbers add to 9. Numbers in the corners are added twice. Once in two lines. Therefore, big numbers in the corners might be a problem. Use some trial and error with these ideas.


Some would like to start by plugging numbers in and use a guess and check strategy.

Others might want to use a little logic and begin by thinking what combination of three numbers add to nine.

Either way a combination of guess and check and reasoning about how the values of numbers are combined to give different sums: Smaller numbers result in smaller sums. Larger numbers result in larger sums. Can be fruitful and result in the following information. The order of the information will vary from person to person.

Relevant information.

4 + 5 = 9, but if they are in the same line, then adding another number will make the sum more than 9. Therefore, 5 & 4 need to be in two different rows.

6 is a big number so small numbers will need to be added to it. The only way to add to 6 and get the sum 9 is, 6 + 1 + 2 = 9. Therefore, 6, 1, & 2 will have to be in one row.

Numbers in the corners are added in two lines. Therefore, big numbers in the corners might be a problem.

With this information, it is fairly easy to use a guess and check strategy and complete the puzzle in a few attempts.

Or continue with a process of elimination strategy and see what might result.

We have 6 + 2 + 1 = 9 that will need to be in one line.

So 3, 4, 5 are left. We already said we can't use 4 with 5 so that means 3 & 4 can be together and 3 & 5 can be together and that is it. So using those combinations we get:

3 + 4 + 2 = 9; 5 + 3 + 1 = 9.

After completing the challenge it is good to review these ideas even if they weren't all used or needed.


Mind Boggler See magic square perimeter


Dr. Robert Sweetland's notes
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