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You have just entered a very large room in $n$-dimensional space ($n \ge 2$). They are labeled $(1, 1, 1, ..., 1)$, $(2, 1, 1, ..., 1)$ and so on, with an infinite number of rooms in each dimension. In one of these boxes $(a_1, a_2, a_3, ..., a_n)$, a cat is hiding. but you do not know which one...