A8. Thirty people of different heights are lined up in a rectangle of six rows of five people each. From each row, we select the shortest, and from these six shortest, we take the tallest; that is Piet. We also select the tallest from each row, and from these six tallest, we choose the shortest; that is Jan. Then we line up all thirty people in order of height, the shortest on the left and the tallest on the right.

Which position can Jan not be in?
A) 21 positions to the left of Piet
D) 19 positions to the right of Piet
B) 19 positions to the left of Piet
E) 21 positions to the right of Piet
C) directly next to Piet

## B-questions
A8. E) 21 positions to the right of Piet. Among the 6 shortest, Piet is the tallest. Therefore, there are at least 5 people shorter than Piet. Jan is the shortest of the 6 tallest, so there are at least 5 people taller than Jan. Therefore, Jan cannot be 21 positions to the right of Piet, because then there would be at least $5+1+20+1+5=32$ people standing next to each other from left to right.

All other positions are possible. Here we only check this for answer C: Jan and Piet stand next to each other. Number the people from 1 to 30 in order of height. Now place people $1,2,3,4$ and 10 in one row and place one of the people $5,6,7,8$ and 9 in each of the other rows. The rest can be distributed randomly over the remaining positions. The shortest of the rows are now 1,5,6,7,8,9, so Piet is number 9. Jan is number 10, because he is the tallest in his row and in all other rows there is someone with a number greater than 10.