You are a tour operator running trips in South America and you have negotiated discounted fares on the following routes:

• Bogatá → Lima
• Lima → Bogatá
• Bogatá → Rio de Janeiro
• Rio de Janeiro → Bogatá
• Lima → Rio de Janeiro
• Rio de Janeiro → Lima
• Manaus → Lima
• Lima → Manaus
• La Paz → Quito
• Lima → La Paz
• Quito → Lima
• Rio de Janeiro → Buenos Aires
• Santiago → Rio de Janeiro
• Buenos Aires → Santiago

How many different tours are possible that travel over all of your discounted routes and start with a flight from Rio to Buenos Aires?

Mathsbombe Competition 2018 is organised by the The Department of Mathematics at The University of Manchester.
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