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MathNet 2022-part-03 — 197 problems (EN–VI) Question 171

Math Olympiad Vault · MathNet 2022-part-03 — 197 problems (EN–VI)

Question 171

A zoo is reconstructing part of their park. In this part, there will be six areas with six species of animals, one in each area. The six species are tigers, lions, elephants, giraffes, zebras and monkeys. The map is as follows:
Question illustration
The tigers and lions cannot be next to each other (this means not in two areas which share a side as border; two areas bordering in a vertex are allowed). The monkeys cannot be next to the tigers and also not next to the lions. The zebras cannot be next to the tigers.
In how many ways can the zoo distribute the six species over the six areas?