As an example to get you thinking, remember the decimal number system is a positional number system. So, with 10 digits (0-9) in 3 positions, we may construct 10*10*10 numbers (that is 1000, from 000-999).

Also, for a date of the form mm/dd, we have 12 possible months and 31 possible days, so that means 12*31 = 372 possible dates. Now, don't get confused -- we just don't use some of the possible mm/dd combinations in a real year [for example 2/30 is not used]. So, to determine the total number of mm/dd combinations that are actually needed, instead of 12*31, we add 31+28(or 29)+31+30+31+30+31+31+30+31+30+31 = 365(or 366). We could also group those into 7*31+4*30+1*28(or 29).

Also, for a date of the form mm/dd, we have 12 possible months and 31 possible days, so that means 12*31 = 372 possible dates. Now, don't get confused -- we just don't use some of the possible mm/dd combinations in a real year [for example 2/30 is not used]. So, to determine the total number of mm/dd combinations that are actually needed, instead of 12*31, we add 31+28(or 29)+31+30+31+30+31+31+30+31+30+31 = 365(or 366). We could also group those into 7*31+4*30+1*28(or 29).

Now, if we wanted dates that look like mm/dd/yy for values of yy from 2017 to 2020 (3 regular years and 1 leap year), we would have 365+365+365+366 instead of 4*365.

O.K., the key to this problem is to determine the number of possible values for each variable.

[note that February has a 28-day version and a 29-day version]

O.K., the key to this problem is to determine the number of possible values for each variable.

**Months: 13**[named January, February, February, March, …, December][note that February has a 28-day version and a 29-day version]

**Day of week for day 1: 7**[positions on calendar are S, M, T,…, S]**Thus, 7*13= 91 plates cover all possibilities of months and starting day [and, eventually, we will use them all].**