Math Problem Statement

Hungarian tram and bus tickets have 9 possible locations for holes.

Passengers need to validate their tickets on their own using a punching machine that creates holes on the ticket. Transportation officials randomly travel around town and ask for the passengers' validated tickets. The tickets do not expire. In theory, the ticket needs to be inserted into the punching machine with the red arrow on top. In practice, this does not matter since the officials do not care about the direction. So, inserting the ticket with the red arrow on the bottom creates the same ticket. A fee evader wants to collect every possible validated ticket and use the appropriate one every time he/she travels. How many different validated tickets are needed if every punching machine in town creates 2 holes on a ticket?

The fee evader needs to collect how many

tickets.

Solution

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Symmetry
Binomial Coefficient

Formulas

Binomial coefficient formula: C(n, k) = n! / (k! * (n - k)!)

Theorems

Combinatorial Symmetry Theorem
Properties of Binomial Coefficients

Suitable Grade Level

Grades 10-12