12 towns divided into 4 zones with 3 town in each. Every town of same zone is connected to the town in its zone with 3 direct telephone lines. The town from one zone is connected to town of other zone by one direct line. How many direct lines are required?

• EACH ZONE HAS 3 TOWNS THEY ARE INTER BY 3 DIRECT LINES =>3*3=9
  THERA ARE 4 ZONES WITH SAME NO. OF TOWNS => 9*4=36
  NOW EACH TOWN OF ONE ZONE IS CONNECTED TO OTHER ZONES TOWN BY ONE DIRECT LINE
  HERE WE CAN NOTE EVERY TOWN OF A ZONE HAS THREE CONNECTIONS TO OTHER ZONE
  HENCE EACH ZONE HAS 9 CONNECTIONS WITH OTHER ZONE AS 4(ZONS)*9(EACH)=36
  NOW 2 OF THE ZONES WIL HAVE CROSS CONNECTIONS (IF YOU DRAW DIAGRAM U CAN NOTICE)
  HENCE 2(TOWNS)*9(EACH)=18
  36+36+18=90 IS ANSWER
• 11 years agoHelpfull: Yes(19) No(2)
• Consider a town in Zone 1. There are 9 towns outside this zone.
  
  Hence 9 lines are required to connect between this town and the other 9 towns.
  
  Similarly, there are 12 towns, each with 9 towns outside its own zone.
  
  So, totally, there will be 9*12 / 2 = 9* 6 = 54 lines inter zone (Divided by 2 comes here because, after half, it is repeated).
  
  Alternate way for inter zone:
  
  1st zone each town has to connect to 9 other towns = 27 lines.
  
  2nd zone – each town has to connect to 6 other zones, as the 1st zone is already accounted for. So 6*3 = 18.
  
  3rd zone – each town has to connect to 3 other zones, as the 1st and 2nd zone is already accounted for. So 3 * 3 = 9.
  
  4th zone is accounted for already.
  
  Hence, totally 26 + 18 + 9 = 54 zones.
  
  So, the total number of lines will be 36 (within zone) + 54 ( inter zone) = 90.
• 11 years agoHelpfull: Yes(14) No(0)
• 1st zone each town has to connect to 9 other towns = 27 lines.
  
  2nd zone – each town has to connect to 6 other zones, as the 1st zone is already accounted for. So 6*3 = 18.
  
  3rd zone – each town has to connect to 3 other zones, as the 1st and 2nd zone is already accounted for. So 3 * 3 = 9.
  
  4th zone is accounted for already.
  
  Hence, totally 26 + 18 + 9 = 54 zones.
  
  So, the total number of lines will be 36 (within zone) + 54 ( inter zone) = 90.
  
• 10 years agoHelpfull: Yes(5) No(0)
• 12 direct lines + 4 = 16
• 11 years agoHelpfull: Yes(2) No(2)
• i got the answer : 66
• 11 years agoHelpfull: Yes(2) No(0)
• we have 12 towns each town has 9 connections then ans = 9*12=108 direct lines
  
• 11 years agoHelpfull: Yes(1) No(3)
• i think 40 is the answer
  
• 11 years agoHelpfull: Yes(1) No(2)
• 4 zones with 3 towns and 3 direct lines so each town has 3 direct lines.
  then totally 12 towns so 3 direct lines * 12 towns =36 direct lines.
  then each town in the zone is connected to another zone town via one direct line.
  consider first town and first zone so it has 3 connection with second zone and 3 connection with third zone and 3 connection with fourth zone . totally in first zone , each town has 9 lines with other zone (towns). then 36+9+9+9=72.the second town is already connected with first zone.it has possibility of third and fourth town so 9 direct lines. then 72+9=81
  and third zone is already connected with first and second zone only possible is fourth zone and it has 9 direct lines.then 81+9=90. and fourth zone is connected with all zones already/........
  ( draw the zones and towns then it is very easy)
• 9 years agoHelpfull: Yes(1) No(0)
• 12 is the answer
• 11 years agoHelpfull: Yes(0) No(2)
• we have 12 towns where each town is connected with other with the help of 9 direct lines as a result we have 27 direct lines(9*9*9)...
  
• 11 years agoHelpfull: Yes(0) No(2)
• answer is 27
• 11 years agoHelpfull: Yes(0) No(0)
• koi theek se bataao yr
• 11 years agoHelpfull: Yes(0) No(0)
• asked only direct lines but not direct telephone lines so 3*9=27 is the answer
  
• 11 years agoHelpfull: Yes(0) No(0)
• Mr hemanth prithvi, you have calculated a single direct line connected to to places a 2, so i think u r wrong.....
• 11 years agoHelpfull: Yes(0) No(0)
• Answer is 38 I think
• 11 years agoHelpfull: Yes(0) No(2)
• each zone town is connected to remaining all towns of zones in 120 ways
• 11 years agoHelpfull: Yes(0) No(0)
• 3*4+9+6+3=30 ans
• 11 years agoHelpfull: Yes(0) No(1)
• total 15
  for each zone we need 3 direct lines so total=12 and
  to connect each zone we need 3 lines ,
  so totally 15 lines
  
• 11 years agoHelpfull: Yes(0) No(0)
• 29..
  in every zone there are 9 lines and one line connected to other zone..
• 11 years agoHelpfull: Yes(0) No(1)
• Sir, please provide the diagram.
• 10 years agoHelpfull: Yes(0) No(0)
• as there are 12 towns so each town is connected with the other 11 towns by 11 direct lines, so for another town, it needs 10 direct lines to connct, then town 3 needs 9 connection town 4 needs 8 connection and so on. so 11+10+9+......+1=66 will be the ans.
• 10 years agoHelpfull: Yes(0) No(0)
• Follow this link for ans:
  http://360dpp.com/12-towns-divided-into-4-zones-with-3-town-in-each-every-town-of-same-zone-is-connected-to-the-town-in-its-zone-with-3-direct-telephone-lines-the-town-from-one-zone-is-connected-to-town-of-other-zone/
• 9 years agoHelpfull: Yes(0) No(0)
• There will be total 12 individual direct lines of each town and one connection to other means 4 connection lines 12+4 = 16 lines total
• 7 years agoHelpfull: Yes(0) No(0)