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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?

 

Please email your answers to deputy-director[at]newton.ac[dot]uk and remember to include your name (or the name of the group that you solved the puzzle with) so that we can publish it on our website if you are one of the first few to successfully solve the problem.  

Answers to all puzzles will be published at the end of the month. 

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