Apologies if this is a basic question, but my math is weak and this is something I've been wondering lately.
This viral Facebook post repeats a long-standing myth that states:
If a thief forces you to take money out of an ATM, do not argue or
resist. What you do is punch in your PIN number backwards. If it's
1234, you'll type 4321. When you do that, the money will come out but
will be stuck in the slot. The machine will immediately alert the
local police without the robbers knowledge and begin taking photos of
the suspect. Every ATM has the feature. Stay safe.
Obviously, this is incorrect, and downright irresponsible. But it's maybe easiest debunked by illustrating just how many PIN numbers would be the exact same if they were reversed, and this got me wondering what exactly that number was.
Pin numbers for banks are generally $4$ digits long and have the possible range of $0000$ to $9999$, which is a total of $10,000$ possible combinations. In as simple terms as possible for someone who's studied very little math, how do I work out how many palindromes are in this range?
Best Answer
A 4 digit palindrome is uniquely determined by the first 2 digits. Since there are 100 such combinations, there are 100 such palindromes.