MathDB

No two of

20

students in a class have the same scores on both written and oral examinations in mathematics. We say that student

A

is better than

B

if his two scores are greater than or equal to the corresponding scores of

B

. The scores are integers between

1

and

10

. (a) Show that there exist three students

A,B,C

such that

A

is better than

B

and

B

is better than

C

. (b) Would the same be true for a class of

19

students?

2