Today is 22 May 2019, the 142nd day of the year.



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Oliver Edgewise has built a most peculiar house. It is in the shape of a large cube with 27 cubical rooms, and the rooms alternate in color – orange and purple! – like a 3-dimensional checkerboard. Moreover, by means of doorways and ingenious spiral staircases, it is possible to get from any room of the house to any adjacent room of the house, whether the adjacency is to the side, above, or below.

Being of a frolicsome disposition, Oliver likes to begin in one room, and then visit every other room in turn, without visiting any room twice, and he has found many ways of doing this. However, he has found that no matter what outside room he begins in, he can never seem to end at the center room after visiting all the others first (and without visiting any room twice).
Today's challenge: Can you help Oliver find a path through the outside rooms that ends in the inside room, or, failing that, show why it can't be done?


Solution to yesterday's challenge

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