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  • Directions for questions from 11 to 14 :   Along the eastern foothills of the Himalayas lie the district of Darjeeling in the state of West Benga

Directions for questions from 11 to 14 :

 

Along the eastern foothills of the Himalayas lie the district of Darjeeling in the state of West Bengal and the state of Sikkim, both of which are considered as a trekker’s paradise. 

 

Five towns in each of them deserve special mention from the point of view of trekking. They are 1) Takdah,  2) Mangan,  3) Sukhiapukhri,  4) Namchi,  5) Mirik,  6) Sarathang,  7) Pelling,  8) Lachung,  9) Sandakphu, and  10) Kurseong. 

 

Each town in either of the district/state is connected to exactly three towns in the other state/district. One town is connected by a 4x4 wheel drive dirt road. The second town is connected by a bicycling route. The third town is connected by a foot-trekking path.

 

The following information is also known about them :

i)   Sarathang has a 4x4 wheel drive dirt road to Sandakphu, which in turn has a bicycling route to Namchi

ii)  Mangan has a foot-trekking path to Kurseong. 

iii) Mangan is not connected to Sukhiapukhri, which is not in the same district/state as that of Mangan

iv) Lachung and Namchi are in the same district/state, and from each of the two towns there is no route to reach Mirik or Kurseong, both of which are towns in a different district/state than the one in which Lachung lies

v)  Sarathang, which belongs to the state of Sikkim, is not connected to Sukhiapukhri which does not belong to the state of Sikkim

Question

For how many of the following pairs of towns is the number of ways of connection more than one, if exactly one town is travelled in between ?

 

 

Option: 1

Mangan and Sarathang

 


Option: 2

Sukhiapukhri and Namchi


Option: 3

Lachung and Mangan


Option: 4

 Sandakphu and Kurseong

 


Answers (1)

best_answer

Since each town in either of the district/state is connected to exactly three towns in the other state/district,

From (v), Sarathang is in state of Sikkim and Sukhiyapokhri is in Darjeeling district

From (i), Sandakphu is in Darjeeling district and Namchi is in state of Sikkim

From (iii), Mangan is in state of Sikkim

From (iv), Lachung is in state of Sikkim and Mirik and Kurseong are in Darjeeling district

a) Hence, Sarathang, Namchi, Mangan and Lachung are in the state of Sikkim, and Sukhiyapokhri, Sandakphu, Mirik and Kurseong are in Darjeeling district. Since there are five towns in each district/state, Takdah and Pelling have to be located one each in the state of Sikkim or Darjeeling district in any order.

b) From (iii) and (v) Sukhiapukhri is not connected to Mangan and Sarathang. So Sukhiapukhri must be connected to Namchi, Lachung and anyone of Takdah or Pelling, depending on which one of the two is in the state of Sikkim.

c) From (iii), Lachung and Namchi are not connected to Mirik and Kurseong. So Lachung and Namchi must be connected to Sukhiapukhri, Sandakphu and anyone of Pelling or Takdah, depending on which one of the two is in Darjeeling district. 

d) Also Mirik and Kurseong must be connected to Mangan, Sarathang and anyone of Takdah or Pelling, depending on which one of the two is in the state of Sikkim.

e) So Sandakphu is connected to Lachung, Namchi and Sarathang. From (i), Sandakphu is connected to Sarathang by 4x4 wheel drive dirt road, and to Namchi by a bicycling route. So Sandakphu must be connected to Lachung by a foot-trekking path.

f) Kurseong is not connected to Lachung and Namchi. So Kurseong must be connected to Mangan, Sarathang and anyone of Takdah or Pelling, depending on which one of the two is in the state of Sikkim. From (ii), Kurseong and Mangan are connected by a foot-trekking path. Sarathang already has a 4x4 wheel drive dirt road connection to Sandakphu (i), so the connection between Kurseong and Sarathang must be a bicycling route. Hence the connection between Kurseong and anyone of Takdah or Pelling must be a 4x4 wheel drive dirt road.

g) Sarathang is connected to Sandakphu by a 4x4 wheel drive dirt road. Sarathang is connected to Kurseong by a bicycling route (f). Sarathang is also connected to Mirik (d). This connection hence must be by a foot-trekking path.

h) The town out of Takdah and Pelling which lies in the state of Sikkim is connected to Mirik, Kurseong (d) and Sukhiapukhri (b). Out of them the connection to Kurseong is a 4x4 wheel drive dirt road (f).  Mirik is connected to Sarathang by a foot-trekking path (g). So the connection of the town out of Takdah and Pelling which lies in the state of Sikkim to Mirik must be a bicycle route. Hence the town out of Takdah and Pelling which lies in state of Sikkim is connected to Sukhiapukhri by a foot-trekking path.

i) Mirik is connected to Sarathang by a foot-trekking path. Mirik is also connected to the town out of Takdah and Pelling which lies in the state of Sikkim by a bicycle route (h). So the connection of Mirik to the other town of Mangan (d) must be by a 4x4 wheel drive dirt road.

j) Mangan is connected to Kurseong by a foot-trekking path (ii). Mangan is connected to Mirik by a 4x4 wheel drive dirt road (i). Hence the other place Mangan must be connected to is anyone of Pelling or Takdah, depending on which one of the two is in Darjeeling district, and that too by a bicycle route.

k) The town out of Pelling or Takdah which lies in the Darjeeling district is connected to Lachung, Namchi (c) and Mangan (j). The connection to Mangan is by a bicycle route (j). Sandakphu is connected to Lachung by a foot-trekking path (e). Hence the town out of Pelling or Takdah which lies in the Darjeeling district must be connected to Lachung by a 4x4 wheel drive dirt road. Thus the connection with Namchi must be by a foot-trekking path.

l) Namchi is connected to Sandakphu by a bicycle route (e). Namchi is also connected to anyone of Pelling or Takdah, depending on which one of the two is in Darjeeling district by a foot-trekking path (k). Namchi is also connected to Sukhiapukhri (b), which must be by a 4x4 wheel drive dirt road.   

l) Lachung is connected to Sandakphu by a foot-trekking path (e). It is also connected to the town out of Pelling or Takdah which lies in the Darjeeling district by a 4x4 wheel drive dirt road (k). Lachung is also connected to Sukhiapukhri (b), which must be by a bicycle route.

m) Sukhiapukhri is connected to Namchi, Lachung and anyone of Takdah or Pelling, depending on which one of the two is in the state of Sikkim (b). Out of them the connection with Namchi is by a 4x4 wheel drive dirt road (k), the connection with Lachung by a bicycle route (l) and the connection with the town out of Takdah or Pelling, depending on which one of the two is in the state of Sikkim, is by a foot-trekking path (h).

Depicting the above results in a tabular form we get :

              Sikkim

 

Sarathang

Namchi

Mangan

Lachung

Takdah / Pelling

 Darjeeling

 

          

Sukhiapukhri

X

4x4 wheel drive             dirt road

X

Bicycle route

Foot-trekking            path

Sandakphu

4x4 wheel drive             dirt road

Bicycle route

X

Foot-trekking            path

X

 

 

Mirik

Foot-trekking            path

X

4x4 wheel drive             dirt road

X

Bicycle route

Kurseong

Bicycle route

X

Foot-trekking            path

X

4x4 wheel drive             dirt road

Pelling / Takdah

X

Foot-trekking            path

Bicycle route

4x4 wheel drive             dirt road

X

 

The X marks indicate no connectivity.

We can see that from Mangan, one can travel to Mirik by a 4x4 wheel drive dirt road and then to Sarathang by a foot-trekking path. Also, from Mangan, one can travel to Kurseong by a foot-trekking path and then to Sarathang by a bicycle route.

From Sukhiapukhri one cannot travel to Namchi with only one town in between.

From Lachung, one can travel to the town out of Pelling or Takdah which lies in the Darjeeling district by a 4x4 wheel drive dirt road and then to Mangan by a bicycle route.

From Sandakphu, one can travel to Sarathang by a 4x4 wheel drive dirt road and then to Kurseong by a bicycle route.

Hence, if exactly one town is travelled in between, the number of ways of connection is more than one only for Mangan and Sarathang.


 

Posted by

Ritika Jonwal

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