TDC1231 DATA COMMUNICATIONS AND NETWORKING
TRIMESTER 1 2015/16
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
Five navvies excavate a 5-metre ditch in 5 hours. How
many navvies are required to dig 100 metres of ditch in
A lumberjack cuts a 5-metre log into 1-metre lengths. If
each cut takes 1.5 minutes, how l
four on each of the five lines. On the right of Fig. 176, four more solutions to the
problem are given.
The uncut trees were disposed as given in Fig. 177. These form five straight rows with
four trees in each.
With Three Straight Lines
The problem is solved as follows:
Into Four Parts
The dash lines show the way in which the ground must be divided (Fig. 187).
To Make a Circle
The joiner has cut each of the boards into four
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
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).
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.
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
Yet Another Parquet
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.
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
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.
If each worker performs half the job individually, the first would need two days more
than the sec
Problems on Purchases
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
Problems on Manual
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
Skilful Cutting and
would be the same.
The aim of the problem is not so much to test your
resourcefulness but the quickness of your thought.
The crescent (Fig. 182) must be divided into six parts
by only two straight
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
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?
At first sight, this ancient problem might seem incongruous as it i
The problem is solved as shown in Fig. 172.
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
Problems with Squares
There is a square pond (Fig. 194) with four old oaks
growing at its corners. It is required to expand the
pond so that its surface area be doubled, the square
shape being retained and the old oaks not destroyed or
' / i l i i i i M
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
Problems on Purchases
cleverest daughter, thirty to the second, and fifty to the
'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
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
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
Distance AB seems to be wider than distance AC.
which is equal to the former.
Holding Fig. 146 at eye level so that you glance
along it, you'll see the picture given on the right.
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.
paper. Shift the figure slightly sidewards and the pins
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
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
J ^ T j Z ^ K .
The answer is s
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
easily see that the new area is twice the earlier, just draw
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
Pranks of Guards
The following is an ancient problem having many
modifications. We'll discuss one of them.