e dial." Now, there are
eleven times in twelve hours when the hour hand is exactly twenty
divisions ahead of the minute hand, and eleven times when the minute hand
is exactly twenty divisions ahead of the hour hand. The illustration
showed that we had only to consider the former case. If we start at four
o'clock, and keep on adding 1 h. 5 m. 27-3/11 sec., we shall get all
these eleven times, the last being 2 h. 54 min. 32-8/11 sec. Another
addition brings us back to four o'clock. If we now examine the clock
face, we shall find that the seconds hand is nearly twenty-two divisions
behind the minute hand, and if we look at all our eleven times we shall
find that only in the last case given above is the seconds hand at this
distance. Therefore the shot must have been fired at 2 h. 54 min. 32-8/11
sec. exactly, or, put the other way, at 5 min. 27-3/11 sec. to three
o'clock. This is the correct and only possible answer to the puzzle.

113.--_Cutting a Wood Block._

Though the cubic contents are sufficient for twenty-five pieces, only
twenty-four can actually be cut from the block. First reduce the length
of the block by half an inch. The smaller piece cut off constitutes the
portion that cannot be used. Cut the larger piece into three slabs, each
one and a quarter inch thick, and it will be found that eight blocks may
easily be cut out of each slab without any further waste.

114.--_The Tramps and the Biscuits._

The smallest number of biscuits must have been 1021, from which it is
evident that they were of that miniature description that finds favour in
the nursery. The general solution is that for _n_ men the number must be
_m_ (_n_^{_n_+1}) - (_n_ - 1), where _m_ is any integer. Each man will
receive _m_ (_n_ - 1)^_n_ - 1 biscuits at the final division, though in
the case of two men, when _m_ = 1, the final distribution only benefits
the dog. Of course, in every case each man steals an _n_th of the number
of biscuits, after giving the odd one to the dog.

INDEX

"Abracadabra," 64.

Age and Kinship Puzzles, 20, 28.

Albanna, Ibn, 198.

Ale, Measuring the, 29.

Algebraical Puzzles. See Arithmetical Puzzles.

Alkalacadi, 198.

Amulet, The, 64, 190.

Archery Butt, The, 60, 187.

Arithmetical Puzzles, 18, 26, 34, 36,
45, 46, 51, 56, 59, 61, 64, 65, 73, 74,
75, 88, 89, 91, 92, 103, 107, 122, 125,
128, 129, 130, 135, 137, 139, 143,
147, 148, 150, 151, 152, 153, 154,