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Summer Maths Puzzles - Friday 16 August - Office Ambles

Office Ambles

The parents had to respond to a couple of work related emails this morning and, to buy themselves some time, they set the children the following problem:

A 2-storey office block has 8 offices, one at each corner A, B, C, D, E, F, G and H of the building.  Corridors run along the edges but not diagonally across the building and each office is connected vertically by a lift (elevator) with the office directly above or below it.

Every Monday morning the janitor, carrying with him 8 pot plants, enters the office block via the front door which leads directly into Office A.  He leaves a pot plant in Office A and then travels randomly from office to office via the lifts and corridors leaving a plant (or at times a second, third plant or fourth plant) in the office he has just entered.

What is the probability that he places the 8th pot plant in office G having placed left one pot plant in each of the other offices along the way?

Can you help the children solve the problem?


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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons