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Amusements in Mathematics

orchard. Of course in picking out a group of ten trees (cherry or plum, as the case may
be) you ignore all intervening trees. That is to say, four trees may be in a straight line
irrespective of other trees (or the house) being in between. After the last puzzle this will
be quite easy.
A man had a square plantation of forty-nine trees, but, as will be seen by the omissions in
the illustration, four trees were blown down and removed. He now wants to cut down all
the remainder except ten trees, which are to be so left that they shall form five straight
rows with four trees in every row. Which are the ten trees that he must leave?
A gentleman wished to plant twenty-one trees in his park so that they should form twelve
straight rows with five trees in every row. Could you have supplied him with a pretty
symmetrical arrangement that would satisfy these conditions?
Place ten pennies on a large sheet of paper or cardboard, as shown in the diagram, five on
each edge. Now remove four of the coins, without disturbing the others, and replace them
on the paper so that the ten shall form five straight lines with four coins in every line.
This in itself is not difficult, but you should try to discover in how many different ways
the puzzle may be solved, assuming that in every case the two rows at starting are exactly
the same.
It will be seen in our illustration how twelve mince-pies may be placed on the table so as
to form six straight rows with four pies in every row. The puzzle is to remove only four
of them to new positions so that there shall be seven straight rows with four in every row.
Which four would you remove, and where would you replace them?
A short time ago I received an interesting communication from the British chaplain at
Meiktila, Upper Burma, in which my correspondent informed me that he had found some
amusement on board ship on his way out in trying to solve this little poser.
If he has a plantation of forty-nine trees, planted in the form of a square as shown in the
accompanying illustration, he wishes to know how he may cut down twenty-seven of the
trees so that the twenty-two left standing shall form as many rows as possible with four
trees in every row.
Of course there may not be more than four trees in any row.