Help me solve this problem:You are designing license plates for your state, population 1 million. What's the shortest license plate you can get away with, using only letters and numbers?

Question

anonymous · Answer

how many plates can you make if you only use one letter?  26, right?

How about 1 letter OR number?  That would be 26 + 10 = 36 choices

How about a plate with 2 characters... 2 letters or numbers?  36 x 36 = 1296

So how many positions do you need to create 1 million plates?

You may have to just try some different answers until you get one that is at least 1 million...

anonymous · Answer

i can't seem to find the right formula yet.

anonymous · Answer

each position on a plate has 36 choices... ten digits and 26 letters.

So a short plate with just 2 positions has 36^2 possibilities...

A longer plate with 8 positions has 36^8 possibilities...

Can you just try some possible plate lengths, or do you need to set up a problem using logarithms?

anonymous · Answer

i think i have it. thanks

anonymous · Answer

ok, glad to help :)