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 nonzero. 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?
Choose the correct choice from the following options: A) 80 B) 78 C) 71 D) 69 E) None
Explanation :   We need to figure out which all numbers cause a confusion when reversed : 0, 1, 6, 8, 9.   1st digit cannot be 0. So, 9 combinations are possible for the 1st digit.   2 digits are distinct. So, 2nd digit cannot be 1st digit.   Hence, again 9 combinations possible for 2nd digit. So, totally, 9 * 9 = 81 numbers are possible.   Since 1st digit is not 0, we can neglect confusions caused by 0, as, if a number with 2nd digit 0 is reversed, it will have its 1st digit as 0, and that is not possible, and hence no confusion. i.e. If we reverse 60, we get 09, but since 0 is not the 1st digit, the agency knows 09 is wrong, and hence it causes no confusion.   The remaining numbers are 1,6,8,9.   Numbers starting with 1: 16, 18, 19 cause confusion.   Numbers starting with 6: 61, 68, 69 cause confusion.   Numbers starting with 8: 81, 86, 89 cause confusion.   Numbers starting with 9: 91, 96, 98 cause confusion.   Now if you think again 69 and 96 does not cause confusion when read upside down. 69 when read upside down is 69, and 96 when read upside down is 96! So, only 10 numbers out of 81 cause confusion.   Hence, there are 71 numbers.   Answer : 71
<result>C</result>
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 nonzero. 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?