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SOLUTIONS
of the game is to bar the centre for the first move of the first player.
In that case the second.player should take the centre at once. This
should always end in a draw, but to ensure it, the first player must
play to two adjoining corners (such as 1 and 3) on his first and
second moves. The game then requires great care on both sides.
111.—The Farmer's Oxen.
Sir Isaac Newton has shown us, in his " Universal Arithmetic,"
that we may divide the bullocks in each case in two parts—one part
to eat the increase, and the other the accumulated grass. The first
will vary directly as the size of the field, and will not depend on the
time ; the second part will also vary directly as the size of the field,
and in addition inversely with the time. We find from the farmer's
statements that 6 bullocks keep down the growth in a 10-acre
field, and 6 bullocks eat the grass on 10 acres in 16 weeks.
Therefore, if 6 bullocks keep down the growth on 10 acres, 24
will keep down the growth on 40 acres.
Again, we find that if 6 bullocks eat the accumulated grass on
10 acres in 16 weeks, then
12 eat the grass on 10 acres in 8 weeks,
48 „ „ 40 „ 8 „
192
„ „ 40 „ 2 „
64 „ „ 40 „ 6 „
Add the two results together (24 + 64), and we find that 88 oxen
may be fed on a 40-acre meadow for 6 weeks, the grass growing
regularly all the time.
112.—The Great Grangemoor Mystery.
We were told that the bullet that killed Mr. Stanton Mowbray
struck the v-ry centre of the clock face and instantly welded
together the hour, minute, and second hands, so that all revolved
193
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