SUCH A GETTING UPSTAIRS.
(
Unclassified Problems.)
In a suburban villa there is a small staircase with eight steps, not
counting the landing. The little puzzle with which Tommy Smart perplexed
his family is this. You are required to start from the bottom and land
twice on the floor above (stopping there at the finish), having returned
once to the ground floor. But you must be careful to use every tread the
same number of times. In how few steps can you make the ascent? It seems
a very simple matter, but it is more than likely that at your first
attempt you will make a great many more steps than are necessary. Of
course you must not go more than one riser at a time.
Tommy knows the trick, and has shown it to his father, who professes to
have a contempt for such things; but when the children are in bed the
pater will often take friends out into the hall and enjoy a good laugh
at their bewilderment. And yet it is all so very simple when you know
how it is done.
Answer:
Number the treads in regular order upwards, 1 to 8. Then proceed as
follows: 1 (step back to floor), 1, 2, 3 (2), 3, 4, 5 (4), 5, 6, 7 (6),
7, 8, landing (8), landing. The steps in brackets are taken in a
backward direction. It will thus be seen that by returning to the floor
after the first step, and then always going three steps forward for one
step backward, we perform the required feat in nineteen steps.
