tmua.me Extreme Set A Paper 2 · Question 6

The integers $1,2,\ldots,27$ are divided into nine groups of three, and each group is replaced by its median. The resulting nine numbers are divided into three groups of three, and again each group is replaced by its median. Finally, the median of the three remaining numbers is taken.

The divisions into groups can be chosen freely at both stages. Which of the following is the complete set of possible final values $m$ ?

AEvery integer

m

with

8\leq m\leq20

BEvery integer

m

with

7\leq m\leq21

CEvery integer

m

with

9\leq m\leq19

DEvery integer

m

with

10\leq m\leq18

EEvery integer

m

with

13\leq m\leq15

m=14

only.

examday

tmua.me Extreme Set A Paper 2 · Q6