## Task 2 - 020722

At a shooting competition of the GST, Günther and Heidrun each fired 5 shots. The following hits were recorded on the targets:

Once the 3, twice the 5, twice the 6, twice the 7, once the 8, once the 9, once the 10.

Günther scored nine times as many points with his last four shots as with his first shot. Heidrun, on the other hand, scored five times as many points with her first four shots as with her last shot; her first two shots together scored exactly as many points as her last two shots together. Günther shot the 9.

a) Who won the competition?

b) Who shot the 10?

The answers must be justified!
In the most favorable case for him, Günther could have shot $10+9+8+7=34$ rings in the last four shots. Since his last four shots must be divisible by nine, he could only have scored 27 rings, and his first shot must have been a 3. Since he hit the 9, he must have scored a total of 18 in the remaining three shots. Therefore, he scored a total of 30 rings, and the 10 is not included.

For Heidrun, 36 of the total 66 rings remain, so she has won.