A palindrome is a number that reads the same forward and back . Here are two palindromes : 494 and 2002 . How many palindromes are there between 100 and 300

Answer 1

To find how many palindromes exist between 100 and 300, we need to look for three-digit numbers in this range that read the same forwards and backwards.

Three-digit palindromes take the form \( aba \), where:

• \( a \) is the first and last digit (hundreds and units place).
• \( b \) is the middle digit (tens place).

For numbers between 100 and 300, \( a \) can only be 1 or 2 because:

• If \( a = 1 \), the number will be in the range 100-199.
• If \( a = 2 \), the number will be in the range 200-299.

Now let's find all the palindromes for both cases of \( a \):

1. When \( a = 1 \):

   • The palindromes are: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191

2. When \( a = 2 \):

   • The palindromes are: 202, 212, 222, 232, 242, 252, 262, 272, 282, 292

Now, let's count the palindromes in each category:

• For \( a = 1 \): There are 10 palindromes (from 101 to 191).
• For \( a = 2 \): There are also 10 palindromes (from 202 to 292).

Adding them together:

• Total palindromes = 10 (from \( a = 1 \)) + 10 (from \( a = 2 \)) = 20.

Thus, there are 20 palindromes between 100 and 300.