PERPLEXITIES. 
Witli Some Easy Puzzles for Beginners. By Henry E. Dudeney. 
160. — THE BARRELS OF HONEY. 
A RICH but honest merchant of Bagdad bequeathed 
all In's possessions to his three sons in equal shares. 
The only difficulty that arose was over the stock of 
honey. There 
were twenty- 
one barrels. 
The instruc- 
tions were 
that not only 
should every 
son receive an 
equal quan- 
tity of honey, 
but should re- 
ceive exactly 
the same number of barrels, and that no honey should 
be transferred from barrel to barrel, on account of 
waste. Now, as seven of these barrels were full of 
honey, seven were half full, and seven were empty, 
this was found to be quite a puzzle, especially as each 
brother objected to taking more than four barrels of 
the same description — full, half full, or empty. How 
was the property fairly divided ? 
1 6 1 . — PAINTING THE LAMP-POSTS. 
Tim Murphy and Pat Donovan were engaged bv the 
local authorities to paint the lamp-posts in a certain 
street. Tim, who was an early riser, arrived first on the 
job, and had painted three on the south side when Pat 
t urned up and pointed out that Tim’s contract was for 
the north side. So Tim started afresh on the north 
side and Pat continued on the south. When Pat had 
finished his side he went across the street and painted 
six posts for Tim, and then the job was finished. As 
there was an equal number of lamp-posts on each side 
of the street, the simple question is : Which man 
painted the more lamp-posts, and just how many 
more ? 
162.— THE LUNATIC STAMP-LICKER. 
The case of Habakkuk Carey, formerly of Camden 
Town, now of Colney Hatch, is not without its pathetic 
side. A very little thing will upset the balance, of some 
alleged minds, 
and in Habak- 
kuk’s case it 
was his in- 
surance card. 
Those words, 
“ Fifth Quar- 
ter,” settled 
his business. 
He experi- 
mented in 
innumerable 
ways, but could not find a fifth quarter anywhere. In 
dissecting an apple he found that he could divide 
the rare and refreshing fruit into four quarters, but the 
tifth always eluded him. He called it “ x,” and said 
it was a thing mathematicians were always trying to 
find, and by George he would find it. He sought 
assistance. The Post Office referred him to the 
Insurance Commissioners, who sent him to the approved 
societies, who sent him elsewhere. After he had left 
home for an indefinite period they found he had divided 
his card into two squares by a thick line, as shown in 
our illustration, and, as he had a supply of 2£d., 3d., 
3 th 
Quarter 
3d., and ;d. stamps, he stuck thirteen of these (using 
some of each) on the card so that the columns, rows, and 
two diagonals of each square (not necessarily the 
same amount in each square) added up alike. 
Can you discover how he did it ? 
163.— THE JOINER’S 
PROBLEM. 
The joiner in the illus- 
tration wants to cut the 
piece of wood into as 
few pieces as possible 
to form a square table 
top, without any waste 
of material. How 
should lie go to work ? 
The proportions are a 
square surmounted by 
a triangle equal to a 
quarter of the square. 
How many pieces would 
you require ? 
Solutions to Last Month s Puzzles. 
155.— THE SIX FROGS. 
MOVE the frogs in the following order : 2, 4, 6, 5, 3, 1 
(repeat these moves in the same order twice more), 
2, 4, 6. This is a solution in twenty-one moves — the 
fewest possible. To find the number of moves neces- 
sary for any even number of frogs, add the number of 
frogs to its square and divide by 2. For an odd 
number of frogs, add three times the number to the 
square of the number, divide by 2, and deduct 4. 
Thus for 3, 5, 7, and 9 frogs the answer is 5, 16, 31, 
and 50 respectively. 
156.— TIIE MOTOR-BICYCLE RACE. 
There were thirteen in the race. Of course, as it 
was a circular track, there were just as many behind 
Gegglesham as before — that is, twelve. 
t 57.— THE DISSECTED CIRCLE. 
It can be done in twelve continuous strokes, thus: 
Start at A in the illustration 
and eight: strokes, forming the 
star, will bring you back to A ; 
then one stroke round the 
circle to B, one stroke to C, 
one round the circle to D, and 
one final stroke to E — twelve 
in all. Of course, in practice 
the second circular stroke will 
be over the first: one : it is 
separated in the diagram, and 
the points of the star not joined to the circle, to 
make the solution clear to the eye. 
158.— THE CYCLISTS’ FEAST. 
There were ten cyclists at the feast. They should 
have paid eight shillings each ; but, owing to the 
departure of two persons, the remaining eight would 
pay ten shillings each. 
159.— THEIR AGES. 
Jack must have been seven years of age and Jill 
thirteen years. 
