170 Combinatorial & Topological Problems- A SWASTIKLAND MAP
Here is a puzzle that the reader will
probably think he has solved at almost
the first glance. But will he be correct?
Swastikland is divided in the manner
shown in our illustration. The Lord
High Keeper of the Maps was ordered
so to color this map of the country
that there should be a different color
on each side of every boundary line.
What was the smallest possible num-
ber of colors that he required?- COLORING THE MAP
Colonel Crackham asked his young
son one morning to color all the
twenty-six districts in this map in such
a way that no two contiguous districts
should be of the same color. The lad
looked at it for a moment, and replied,
"I haven't enough colors by one in
my box."
This was found to be correct. How
many colors had he? He was not
allowed to use black and white-
only colors. - PICTURE PRESENTATION
A wealthy collector had ten valuable pictures. He proposed to make a
presentation to a public gallery, but could not make up his mind as to how
many he would give. So it amused him to work out the exact number of dif-
ferent ways. You see, he could give anyone picture, any two, any three, and
so on, or give the whole ten.
The reader may think it a long and troublesome calculation, but 1 will give
a little rule that will enable him to get the answer in all such cases without
any difficulty and only trivial labor.