## Task 2 - 120622

A total of 2650 M in bonuses were awarded to 11 workers of a state-owned enterprise, with bonuses of 150 M, 250 M, 350 M, 400 M, and 500 M, and each bonus level was awarded at least once.

Determine the number of workers who received 150 M each!

Since each bonus level was represented at least once, there was at least one worker who received 150 M, one who received 250 M, one who received 350 M, one who received 400 M, and one who received 500 M.

These five workers thus received a total of 1650 M.

For the remaining 6 workers, exactly 1000 M remained.

If each of these 6 workers had received exactly 150 M, that would have been a total of 900 M. Therefore, at least one of the 6 workers must have received more than 150 M.

According to the problem, he must have received at least 250 M. For the remaining 5 workers, at most 750 M remained, so no further worker among the five could have received more than 150 M. Consequently, the number sought is 6.

# Task 3 - 120623

After a solidarity collection for Vietnam, the Thälmann Pioneers Rita, Werner, Margot, Beate, and Jan compared their collection results. They found:

(1) Beate collected more than Jan but less than Werner.

(2) Rita collected 13 M, which was less than what Jan collected.

(3) Beate's collection result was 4 M higher than Rita's.

(4) Margot collected 2 M less than Werner but 1 M more than Jan.

(5) Two Pioneers achieved the same collection result.

Determine the collection result of each of the five Pioneers.
The collection results of the pioneers are denoted by $r, w, m, b, j$ (in Marks). According to the problem:

(1) $w>b>j$

(2) $j>r ; r=13$

(3) $b=r+4$

(4) $w=m+2 ; m=j+1$

From (2) and (3), it follows that $b=17$. From (1) and (2), it follows that $w>b>j>r$, and from (4) $w>m>j$, and from this as well as (5) $m=b$, so $m=17$.

Therefore, Werner collected 19 M, Beate and Margot each 17 M, Jan 16 M, and Rita 13 M.