TDC1231 DATA COMMUNICATIONS AND NETWORKING
TRIMESTER 1 2015/16
TUTORIAL 01
Tutorial Exercises
1. Assuming 6 devices are arranged in a mesh topology. How many cables are
needed? How many ports are needed for each device?
2. Draw a hybrid topology with a bu

Problems on Manual Work
Navvies
Five navvies excavate a 5-metre ditch in 5 hours. How
many navvies are required to dig 100 metres of ditch in
100 hours?
Lumberjacks
A lumberjack cuts a 5-metre log into 1-metre lengths. If
each cut takes 1.5 minutes, how l

Answers
Figure 176
four on each of the five lines. On the right of Fig. 176, four more solutions to the
problem are given.
An Orchard
The uncut trees were disposed as given in Fig. 177. These form five straight rows with
four trees in each.
Figure
ill

180-181
Answers
With Three Straight Lines
The problem is solved as follows:
Figure 186
Into Four Parts
The dash lines show the way in which the ground must be divided (Fig. 187).
Figure 187
To Make a Circle
The joiner has cut each of the boards into four

Answers
We can thus easily find the sum of the weights of No. 1, No. 2, No. 4, and No. 5:
110 kg + 121 kg = 231 kg. Subtracting this number from the total weight of the bags
(289 kg) gives the weight of No. 3, namely-58 kg.
Further, from the sum of No. 1

Skilful Cutting
and
Connecting
a square from five identical triangles like the ones you
have just used (the base is twice as long as the height).
You may cut one of the triangles into two parts but the
other four must be used as they are (Fig. 185b).
Figu

166-165
Brain-Twisting
Arrangements
and Permutations
How could they make it?
Observe the following rules:
(1) each animal may make several leaps at once;
(2) two animals may not seat on the same stump,
therefore they must only leap on a vacant stump.
Furt

176-177
Answers
The White
Mouse
The cat should first eat the mouse at which it is looking, i. e. the sixth one from the
white. Try it by beginning with this mouse and cross out every 13th mouse. You'll see
that the white mouse will be the last to be cross

186-187
Answers
Yet Another Parquet
Maker
The test might only show that the quadrilateral in question has right angles, i. e. that
it is a rectangle. But it fails to verify that all its sides are equal, as is seen in Fig. 200.
Figure 200
A Seamstress
The

160-161
Optical
Illusions
Figure 155
Figure 156
On the left you see a convex cross, on the r i g h t - a
concave one. But turn the book upside down and the
figures will change their places. Actually the figures are
identical, only they're shown at differe

190-187
This is the actual duration of work of the first peeler, the second one worked for
70 + 25 = 95 minutes.
In fact: 3 x 70 + 2 x 95 = 400.
Two
Workers
If each worker performs half the job individually, the first would need two days more
than the sec

192-193
Problems on Purchases
and Prices
How Much are the Lemons?
Three dozen lemons cost as many roubles as one can
have lemons for 16 roubles.
How much does a dozen lemons cost?
Raincoat, Hat and Overshoes
A raincoat, hat and overshoes are bought for 14

188-189
Problems on Manual
Work
were done by each of them separately, then the first
would take four days more than the second.
How many days would each of them take to perform
the job individually?
The problem permits of a purely arithmetic solution
with

178-179
Figure 181
Skilful Cutting and
Connecting
would be the same.
The aim of the problem is not so much to test your
resourcefulness but the quickness of your thought.
Crescent
The crescent (Fig. 182) must be divided into six parts
by only two straight

Brain-Twisting Arrangements
and Permutations
In Six Rows
You may have heard the funny story that nine horses
have been put into 10 boxes, one in each. The problem
that is now posed is formally similar to this famous
joke, but it has a real solution *. You

Problems on Purchases
and Prices
Figure 205
one bought two and the other bought three. Given that
the second bought twice as much beer as the first,
which barrel wasn't sold?
Selling Eggs
At first sight, this ancient problem might seem incongruous as it i

172-173
Answers
Nine
Zeros
The problem is solved as shown in Fig. 172.
Figure 172
Thirty Six
Zeros
As it's required to cross out 12 of the 36 zeros, we'll have 3612, i.e. 24 zeros with
four zeros in each row.
The remaining zeros will be arranged as follow

182-183
Answers
Figure 192
To Make Up a Square
The solution of the first problem is shown in Fig. 193a. The case of triangles is given
in Fig. 193b. One triangle is first cut up as shown.
Figure 193

Problems with Squares
A Pond
There is a square pond (Fig. 194) with four old oaks
growing at its corners. It is required to expand the
Figure 194
pond so that its surface area be doubled, the square
shape being retained and the old oaks not destroyed or
s

Answers
Figure 173
I
w
w
If*
I
T
' / i l i i i i M
Eight
Letters
The least number of moves is 23. These are as follows:
A B F E C A B F E C A B D H G A B D H G D E F
Squirrels and Rabbits
Shown below is the shortest way of the rearrangement The first numb

194-187
Problems on Purchases
and Prices
cleverest daughter, thirty to the second, and fifty to the
third, saying:
'You should agree beforehand on the price at which
you'll sell the eggs and stick to it. All of you should
adhere to this price but I hope t

168-165
Brain-Twisting
Arrangements
and Permutations
The commander's tent is guarded by sentries housed
in eight other tents (Fig. 166). Initially in each of the
tents there were three sentries. Later the sentries were
allowed to visit each other and thei

170-165
Brain-Twisting
Arrangements
and Permutations
to see the result. Much to his dismay he found the
orchard almost devastated: instead of the 20 trees the
workman had left only 10 and cut 39.
"Why have you cut so many ? You were told to leave
20 trees

156-157
Optical
Illusions
Figure 143
Figure 144
Distance AB seems to be wider than distance AC.
which is equal to the former.
Figure 145
A
0
B
Holding Fig. 146 at eye level so that you glance
along it, you'll see the picture given on the right.
Close one

Brain-Twisting
Arrangements
and Permutations
two castles protected within the walls. The architect
objected that it was impossible to satisfy the condition
whilst the 10 castles had to be arranged four in each of
the five walls. But the prince insisted.
A

Optical
Illusions
Figure 146
paper. Shift the figure slightly sidewards and the pins
will swing.
Figure 147
Figure 149
Figure
148
If you view this figure for a long time, it'll seem to
you that the two cubes at the top and at the bottom
stand out alternat

Answers
A Clock Dial
As the sum of all the numbers on the face of the dial is 78, the sum of each of the six
sections mast be 78-f-6 = 13. This facilitates finding the solution that is shown in
Fig. 189.
Figure 189
J ^ T j Z ^ K .
Crescent
The answer is s

n
Answers
A Pond
It is possible to double the surface area of the pond with the square shape retained
and the oaks intact. The accompanying figure shows how this can be done. You can
Figure 197
easily see that the new area is twice the earlier, just draw

158-159
Figure
150
Optica!
Illusions
touching the walls from the inside, the box being open
at the bottom.
The intersections of the white lines in this figure seem
to have yellowish square spots that appear and
disappear, as if flashing. In actuality, the

Brain-Twisting
Arrangements
and Permutations
Figure 165
Jacob's garden
Peter's garden
Paul s
garden
Pranks of Guards
The following is an ancient problem having many
modifications. We'll discuss one of them.
Figure 166