Suppose a 4-digit PIN must be formed using the digits 0 through 9.
A palindrome reads the same forward as backwards. For example 5885 is a palindrome, but 1231 is
not a palindrome. List every such PIN that is a palindrome. How many are there? Can you think of
a more clever way to count them without listing every single one?

Question

Suppose a 4-digit PIN must be formed using the digits 0 through 9.
A palindrome reads the same forward as backwards. For example 5885 is a palindrome, but 1231 is
not a palindrome. List every such PIN that is a palindrome. How many are there? Can you think of
a more clever way to count them without listing every single one?

ganeshie8 · Answer

What have you tried so far ?

ganeshie8 · Answer

Suppose a number starts with $23$
can you guess the remaining two digits ?

bee_see · Answer

I was able to solve it...the answer is 90, right?

zenmo · Answer

What does the solution say?

zenmo · Answer

if you could message me it

bee_see · Answer

(9x1)x(10x1)

bee_see · Answer

first digit=last digit. 9 possibilities each. counted once. 
middle digits=10 possibilies

zenmo · Answer

0110 0220 0330 0440 0550 0660 0770 0880 0990 
1001 1221 1331 1441 1551 1661 1771 1881 1991
2112, and so on. ..

zenmo · Answer

your answer of 90 sounds correct

zenmo · Answer

But, then I'm not sure, sorry. :(

whpalmer4 · Answer

No, 90 is not correct.  Let's think about this.  If you need a 4-digit pin which is a palindrome, the last two digits are the first two digits, reversed.  How many 2-digit sequences can you construct with the digits 0-9?  For each 2-digit sequence, there will be 1 4-digit palindrome.

Remember that we are not talking about numbers here, but rather sequences of digits.