## Task 4 - 250514

In each of the figures a), b), c), the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 are to be entered into the circles.

Each of these numbers should (in each such entry) occur exactly once. For some circles, the number to be entered is already specified. Furthermore, for each entry, the following should apply:

If you add the four numbers on each side of the triangle, the sum should be the same for each of the three sides.

a) Find an entry in Figure a) where the sum for each of the three sides is 17!

b) Find as many entries as possible in Figure b) where the sum for each of the three sides is 21!

c) Find as many entries as possible in Figure c) where the sum for each of the three sides is the same! For each of these entries, give this value!

a)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=314&width=369&top_left_y=865&top_left_x=455)
b)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=320&width=357&top_left_y=862&top_left_x=878)
c)

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=323&width=351&top_left_y=861&top_left_x=1292)
Figure a shows a solution to task a);

the figures b 1, 2, 3, 4 show four solutions to task b);

the figures c 1, 2 show two solutions to task c), in both of these solutions, the sum for each side of the triangle is 20.

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=306&width=348&top_left_y=1463&top_left_x=294)

$a$

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=303&width=331&top_left_y=1459&top_left_x=680)

$b 1$

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=299&width=348&top_left_y=1461&top_left_x=1045)

$b 2$

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=303&width=343&top_left_y=1459&top_left_x=1416)

$b 3$

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=314&width=352&top_left_y=1836&top_left_x=475)

$b 4$

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=302&width=351&top_left_y=1845&top_left_x=858)

$c 1$

![](https://cdn.mathpix.com/cropped/2024_06_06_b85a894aa8dbf722a7b3g-0108.jpg?height=309&width=354&top_left_y=1844&top_left_x=1225)

$c 2$

Solutions from the 1st Round 1985 adopted from [5]

### 2.26.2 2nd Round 1985, Class 5