166 Combinatorial & Topological Problemsappear to be somewhat out of the
game, as the only purpose it serves is
to complete one row. So he set to
work on a better arrangement, and in
the end discovered that he could plant
thirteen trees so as to get nine rows of
four. Can the reader show how it
might be done?..
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- THE TWENTY PENNIES
If sixteen pennies are arranged in the form of a square there will be the
same number of pennies in every row, column, and each of the two long
diagonals. Can you do the same with twenty pennies?- TRANSPLANTING THE TREES
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A man has a plantation of twenty-two trees arranged in the manner here
shown. How is he to transplant only six of the trees so that they shall then
form twenty rows with four trees in every row?
- A PEG PUZZLE
The illustration represents a square mahogany board with forty-nine holes
in it. There are ten pegs to be placed in the positions shown, and the puzzle