An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?

• Confusion will exist in numbers having digits 0,1,6,8,9
  Total combinations between 00 and 99 are 100
  And the Numbers which will cause confusion are
  01,06,08,09,10,16,18,19,60,61,66,68,80,81,86,89,90,91,98,99
  No confusion numbers=100-20=80
  Note that we eliminated 00,11, 69,96 and 88 because they will not cause confusion.
• 8 years agoHelpfull: Yes(11) No(1)
• Total digits that can be formed = 10C1 * 10C1 = 100.
  The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.
  
  So codes that can create confusion are:
  01, 06, 08, 09
  10, 16, 18, 19
  60, 61, 66, 68 (69 would still be 69 when inverted)
  80, 81, 86, 89
  90, 91, 98, 99 (96 would still be 96 when inverted)
  
  There are 20 such numbers.
  Required numbers = 100 - 20 = 80
• 8 years agoHelpfull: Yes(9) No(0)
• from 10 to 99 total 2 digit no is 89.
  now if 91 show 16 then
  from 10 to 20 no in confusion posibility is 2
  same as 21 to 30 is =2
  31 to 40 is=2
  41 to 50 is=2
  51 to 60 is=3
  61 to 70 is=9
  -----
  --- upto 99 total no is=32 so,89-32=57 no don't have confusion posibility.
• 8 years agoHelpfull: Yes(2) No(7)
• numbers with confusion 01,06,08,09,10,16,18,19,61,66,68,80,81,86,89,90,91,98,99
  there are total 20 numbers with confusion
  so, 100-20=80
• 8 years agoHelpfull: Yes(1) No(1)
• 01,10,06,90,09,60
  80
• 8 years agoHelpfull: Yes(0) No(1)