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

1) 25
2) 75
3) 80
4) None of these

• Parts of this question are open to interpretation. One distinction is whether you can have a leading zero and have that be a valid "two-digit" code. That's probably why some people use 90 numbers (10 to 99) and others use 100 (00 to 99).
  
  I'm going to use the classic definition of 10-99 as two-digit numbers. So there are 90 numbers to consider.
  
  Next you have to figure out which numbers are considered reversible numbers. Generally I would say that 0, 1, 6, 8 and 9 are reversible. They look the same or like another number when turned upside down. The other numbers (2, 3, 4, 5 and 7) would be immediately recognized as upside down in most fonts. An exception might be on a LCD display (like an alarm clock) where the 2 and 5 would also work, but I'll ignore this.
  
  If we assume that the number can't have a leading zero, then 0 is irrelevant. A number like 80 would become 08 and we know that's not a valid two-digit number. Likewise 60 would become 09 which is not a valid two-digit number. So we can ignore 0.
  
  That leaves 1, 6, 8 and 9 as problem digits. We also only have to consider cases where both digits are in this subset. We don't have to worry about something like 78, because the 7 won't look right upside down.
  
  Let's consider all 16 pairings of these digits:
  11, 16, 18, 19, 61, 66, 68, 69, 81, 86, 88, 89, 91, 96, 98, 99
  
  Now pick out the 4 pairs that won't matter.
  11 will look like 11
  69 will look like 69
  88 will look like 88
  96 will look like 96
  
  So there are only 12 numbers that are problems.
  
  Subtracting from 90, I would say there are 78 that could cause confusion.
  
  Answer (assuming that leading zeroes are NOT allowed):
  78 numbers wouldn't cause confusion.
  12 numbers would cause confusion
  
  16 91
  18 81
  19 61
  61 19
  66 99
  68 89
  81 81
  86 98
  89 68
  91 16
  98 86
  99 66
  
  UPDATE:
  
  I thought about this further and think the author must be allowing for leading zeroes in the codes, then we have 100 numbers to consider and 0 is a problem digit.
  
  Reversible digits are {0, 1, 6, 8, 9}
  
  There are 25 pairings of these digits:
  00, 01, 06, 08, 09, 10, 11, 16, 18, 19, 60, 61, 66, 68, 69, 80, 81, 86, 88, 89, 90, 91, 96, 98, 99
  
  Of these, we can eliminate 5 pairs that look like themselves:
  00, 11, 69, 88, 96
  
  So that leaves 20 problem numbers. And then we subtract from 100 leaving 80.
  
  Revised answer (assuming that leading zeroes ARE allowed):
  80 numbers wouldn't cause confusion
  20 numbers would cause confusion
  
  01 10
  06 90
  08 80
  09 60
  10 01
  16 91
  18 81
  19 61
  60 09
  61 19
  66 99
  68 89
  80 08
  81 18
  86 98
  89 68
  90 06
  91 16
  98 86
  99 66
  
  Answer:
  c) 80 (or 08, if you accidentally look at it upside down. :)
• 7 years agoHelpfull: Yes(12) No(1)
• actually can solve as 10P2 as out of 10 letters using 2 letters.so its 90.(as 0 can be the 1st letters as they are codes not any valuable nos)
  now same lookng digits are 0,1,6,8 and 9 while reverted. so ,using them forming 2 digits codes are 5P2=20.
  this will be diveded by 2 =10 (cos using this five no 20 codes possibility while out of which exactly 1/2 are the reverted of 20 ie 10) so to remove these 10 we deduce 10 from 90
  ie. 90-10=80.
  is the ANSWER 80.
• 9 years agoHelpfull: Yes(10) No(2)
• confusing codes from 100 two digit numbers
  
  01-10,06-90, 08-80, 09-60, 16-91, 18-81, 19-61, 66-99, 68-89, 86-98.
  
• 11 years agoHelpfull: Yes(3) No(1)
• total possible codes:- 10*10=100
  
  digits that can be confused-0,1,6,8,9
  
  so, confusing codes=5*5=25
  
  but some are exceptions:
  69 is seen as 69 when inverted upside down
  88 is seen as 88 when inverted upside down
  96 is seen as 96 when inverted upside down
  00 is seen as 00 when inverted upside down
  11 is seen as 11 when inverted upside down
  
  so total confusing code=25-5=20
  
  so TOTAL non-confusing code=100-20=80
  
  80 is the ans.
• 6 years agoHelpfull: Yes(2) No(0)
• 80 codes are there such that there is no possibility of any confusion.
  
  The digits which create confusion are...... 0,1,6,8 and 9.
• 11 years agoHelpfull: Yes(1) No(0)
• 80
  confusing one are:0,1,6,8,9
  
• 9 years agoHelpfull: Yes(0) No(0)
• I am not certain I understand this question. However, the numbers which cannot be confused with another number, when inverted, are 2, 3, 4, 5, and 7. These could be combined with any of the other numbers, 0, 1, 6, 8, and 9 and still avoid confusion. Note that 0, 1 and 8 could be confused in a two digit number because 01 and 81 would look like 10 and 18, respectively, upside down. So, for instance, one could write 02 and 20 and neither could be confused, assuming that 2 could not be confused with 5 (that both are carefully, and not sloppily written). This would eliminate two digit combinations that included only the numbers that could be confused.
  The total number of combinations of 2-digit numbers, 0 - 9 is
  10^2 = 100. The total number of 2-digit numbers, using the confusable numbers is 5^2 = 25 since there are 5 numbers that can be confused up from down. So 100 - 25 = 75. I would say the answer was b).
  If someone declared that 2 could be confused with 5 when inverted, this would increase the confusable number list to 6 numbers, Since 6^2 = 36, and the total 2-digit array of useable numbers would be reduced to 100 - 36 = 64.
• 6 years agoHelpfull: Yes(0) No(0)
• First let us consider numbers which will cause confusion ie, 0,1,6,8,9
  starting with 0_ (we can place 1,6,8,9 a total 4 numbers) =4
  " " 1_ (we can place 1,6,8,9 a total 4 numbers) =4
  " " 8_ ( " " " 0,1,6,9 a total 4 numbers) =4
  " " 6 (we can place 0,1,6,8 a total 4 numbrs) =4 (here we cant place 9 bcz 69 reverse is 69 )
  " " 9 ( we can place 0,1,8,9 a total 4 numbrs) =4( " " " " 6 " " " " " )
  so total confusing numbers are => 4+4+4+4=20
  now not confusing numbers = total numbers - confusing numbers => 100-20 = 80 is the ans.
• 5 years agoHelpfull: Yes(0) No(0)
• I think digits such as 0,1,6,8,9 are reversible and give meaningful output when reversed so all their combinations such as
  01,06,08,09,10,60,80,90,16,18,19,61,81,91,68,69,86,89,96,98,66,99 can create confusion... so my answer would be 100-22=78 , but I think that they had not considered 66 and 99 so their answer could be 80.
• 5 years agoHelpfull: Yes(0) No(0)