An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, ... , 9 such that the first digit of the code is non-zero. The code, handwritten on a slip, can however potentially create confusion, when read upside down for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?

1) 80
2) 78
3) 69
4) 71

• Since first digit can't be zero, so there are only 90 possibilities.
  10 to 99 i.e count is 90.
  
  Moreover, this includes 9 wrong possibilities i.e 11,22,33,44,55,66,77,88,99.
  
  So now the possible count is 81.
  
  1 more fact, there are 5 digits which can cause confusion i.e 0,1,6,8,9 and since first digit can't be zero.
  so confusing number of digits are (3*4 + 4) i.e (last digit is not zero + last digit is 0) i.e 16.
  Among these 10,60, 80, 90 are not confusing because for eg if number is 10 & someone is holding it upside down then it seems to be 01 which can't be possible so it means he/she is holding the number wrongly. There is no confusion.
  
  So there are 12 numbers left which are confusing. One last thing, 96 and 69 are confusion. Some had commented that they are not confusioning but they are.
  
  So the answer is :-
  = Total possible - confusing numbers
  =81-12 = 69
• 11 years agoHelpfull: Yes(2) No(0)