How many positive integers less than 100 can be written using only the digits 6, 7, 8, and 9?

Question

I would prefer a quick-ish way to work it out as this is for Academic Team meets, in which math questions must be done in either 5 or 10 seconds maximum.

Answer 1

Basically, this question is really asking how many ways you can pair the digits if you allow repeats.

 

You have four digits for the tens spot and four digits for the ones spot.  The counting principle tells us to multiply the number of options in each slot to determine the total number of options.

 

Therefore, 4 times 4 = 16.  There are 16 positive integers less then 100 written with only those digits.