An intelligence agency forms a code of two distinct digits selected from 0, 1,....,9 such that the first digit of the code is non-zero. The code, handwritten on a slip, however, can potentially create confusion when read upside down, e.g. the code 91 may appear as 16. How many codes are there for which no such confusion can arise?
a) 80 b) 63 c) 71 d) None of these

• 71
  
  10 to 99... total 90 2 digit numbers are there out of which 9 are having same two digits like 11,22,33 ...99 which are not allowed.
  Balance 81 codes are there.
  
  Now 16, 18, 19, 81, 86, 89, 61, 68, 91 ,98 are confusing codes.
  
  so 71 codes are there which do not create any confusion.
• 12 years agoHelpfull: Yes(24) No(8)
• garima is right.....here 69 and 96 are not included bcoz they are similar when they ar read as upside down
• 12 years agoHelpfull: Yes(8) No(1)
• Ans:69
  We have to select 2 distinct digits that should not start with zero. so, the possible numbers are from 10 to 99,Then total numbers are 90
  
  The numbers 11,22,33.......99 making confusion and also the numbers 16,18,19,61,68,69,81,86,,89,91,96,98 making confusion.
  
  totally 21 numbers making confusion.
  
  The answer is 90-21=69
• 6 years agoHelpfull: Yes(3) No(1)
• 10 60 80 90 69 and 96 are also excluded
• 12 years agoHelpfull: Yes(2) No(5)
• 10 to 99... total 90 2 digit numbers are there out of which 9 are having same two digits like 11,22,33 ...99 which are not allowed.
  Balance 81 codes are there.
  Now 16,18,19,61,68,69,81,86,89,91,96,98 total no =12 confusing codes
  Required ans = 81-12=69.
  You can check answer on below link
  
  http://www.elitmuszone.com/elitmus/permutation-and-combinations-set-2/
  
• 9 years agoHelpfull: Yes(2) No(1)
• the ans is 63. bcoz it is mentioned that the digits are distinct. so yu have to exclude 22,33,44,55,66,77,88 and 99 also.
  therefore 71-8= 63
• 12 years agoHelpfull: Yes(1) No(7)
• Answer = 69,
  
  In given question they are given that two distinct digits,so we take from 10 to 99 but distinct digits means that two numbers are different e.d 11,22,33,...99 are not comes under a distinct numbers and first value is not zero as given in question so the total numbers possible in between is 9*9 which means 1 to 9 from first element and 1 to 9 from another element so 9*9=81 confusing element are 16,18,19,61,68,69,81,86,89,91,96,98. So there are 12 elements
  Answer = total elements - confusing elements
  Answer=81-12
  Answer=69
• 6 years agoHelpfull: Yes(1) No(0)
• The digits which create confusion are 0, 1, 6, 8, 9.
  The total number of two-digit codes having distinct digits and first digit non-zero.
  1st place 2nd place
  9 option 9 options ( one digit is
  (1 to 9) already used out of 1 to 9 and 0 is
  included)
  = 9×9 =81 such codes
  Total number of two digit codes which can create confusion.
  1st digit 2nd digit
  4 options 4 options
  (1, 6, 8 or 9) (one digit is already used out or
  1, 6, 8 and 9 and 0 is
  also included )
  =4×4=16
  But these 16 two-digit codes include 69 and 96, which create no confusion. Apart from these, 10, 60, 80 and 90 are such two digit codes as create no confusion because these codes are no expected.
  Hence total number of two-digit codes which create no confusion
  =81-16+6=71
  
  source:toppr
• 4 years agoHelpfull: Yes(0) No(0)