The solution to placing the digits 1, 2, 3, 4, 5, and 6 in the circles with a sum of 12 on each side:
4
/ \
2 5
/ \ / \
1 3 6
Limited Configurations: As the hint suggests, there are only a few possible configurations due to the limited number of digits and the required sum. You can start by analyzing which pairs of digits add up to 12.
Key Pair: The crucial pair is 4 + 5 = 9. This pair must appear on one side of the triangle, leaving 3 for the remaining number.
Placement of 4 and 5: Since the sum on each side needs to be 12, the remaining number needs to be 3. Therefore, 4 and 5 must be positioned opposite each other on the triangle's base.
Completing the Triangle: With 4 and 5 on the base, place 3 on the opposite side. Now, you can fill the remaining positions with the remaining digits: 2 and 1 on the left side, and 6 on the right side.
This configuration ensures that the sum of the digits on each side is 12:
Base: 4 + 5 = 9
Left side: 2 + 3 + 1 = 6
Right side: 5 + 6 = 11
Therefore, the solution is the one shown above, with 4 at the top, 2 and 5 forming the left base, 1 and 3 forming the right base, and 6 on the right side.