Advanced: It is possible to pair up all the numbers from 1 to 70 so that the positive difference between the numbers in each pair is always the same. For example, one such pairing up is (1,2), (3,4), (5,6),....(69,70). Here the common difference is 1. What is the sum of all such common differences?

• there is a 5 combinations in 1to 10 i.,e(1,2),(3,4),(5,6),(7,8)(9,10)
  11t020 =5
  21to30=5
  31to40=5
  41t050=5
  51to60=5
  61to70=5
  there is now total combinations are 35.
  the difference between each combination is 1 so sum of all common difference is 35.
  ANS=35
• 5 years agoHelpfull: Yes(2) No(6)
• given range is 1 to 70
  conditios:
  1.common difference is 1
  2.number os such pairs.
  let us consider the range to be 1 to 10
  when the common difference exceeds 5 the condition1 will not get satisfied.
  for a range 1 to n we have n/2 common differences.
  for 70, 70/2=35 common differences will satisfy condition 1.
  the second thing here is to find the sum of such pairs.
  =1+2+3+.............+35
  =35(35+1)/2
  =630.
• 5 years agoHelpfull: Yes(1) No(6)
• Now consider the first 3 pairings i.e. (1,2),(3,4),(5,6), here we have the last number as 6 and the sum of their common differences as 1+1=2. In the similar was for 4 pairings we will have the last number as 8 and the sum of their common differences as 1+1+1=3
  
  Thus we can say that for similar such cases the sum of common diff. will be =(last num in the pairing / 2)-1
  
  Therefore we have the answer for the above question as =(70/2)-1 = 34.
• 3 years agoHelpfull: Yes(0) No(0)
• The question is asking for the sum of differences which are possible for such pair
  Solution : (1, 2), (3, 4), (5,6) ...................(69, 70) -> common difference = 1 ;
  here for common difference 1 we have to make pair up to 2
  if common difference would be three then we have to make pair up to 6 which is not divisible by 70
  so we have to find the no. whose double can divide 70
  Here we have
  1 -> 1*2 = 2
  5 -> 5*2 = 10
  7 -> 7*2 = 14
  so the answer is 1+5+7 = 13 Ans.
• 2 years agoHelpfull: Yes(0) No(0)
• The no of total pairs in the sequence of 1 to 70 is 70/2=35
  And the difference between the numbers in each pair is same which is 1.
  Therefore the sum of all such common differences is 1*35=35
• 1 Month agoHelpfull: Yes(0) No(0)