NOTE: Here confusion refers to the fact that the number if written on a piece of paper would appear as different number if viewed upside down. 18 may be viewed as 81 and so on
Can anyone find a generalized way to calculate the number of numbers which cause/don't cause confusion when rotated?
For $2$ digits... Total possible numbers... $9\times 10=90$ Digits causing confusion $= 4 (1,6,8,9)$ Possible numbers.... $4\times 4 = 16$ (Number can be confusing IFF both the digits are confusing, $0$ not considered because the number can't be single digit) Exceptions... $11, 69, 88, 96$
Soln... $90-16+4= 78$
Is there a generalized solution for $3$ digits? Because the exceptions would be much harder to find.. Number of possible confusions for 3 digits are... $4\times 5\times 4 = 80$ ($0$ can't be first or last)