MathDB

A maths teacher has

10

cards with the numbers

1

10

on them, one number per card. She places these cards in some order in a line next to each other on the table. The students come to the table, one at a time. The student whose turn it is goes once through the line of cards from left to right and removes every card she encounters that is (at that moment) the lowest card on the table. This continues till all cards are removed from the table. For example, if the line is in order

3

1

4

5

8,

6

9

10

2

7

from left to right, the first student takes cards

1

and

2

. Then the second student comes who, in our example, takes the cards

3

4

5

6

, and

7

. The third student then takes the cards

8

9

, and

10

. Let

A

be the number of sequences of cards that the teacher can choose so that exactly nine students get a turn to pick cards. Let

B

be the number of sequences of cards that the teacher can choose so that exactly two students get a turn to pick cards. Prove that

A = B

Problem Statement