101
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All the odd numbers of the odd tens plus the odd numbers less than 10.
There are 5 odd numbers in each ten
There are 5 odd tens, plus the numbers less than 10
giving 5 x (5+1) = 30 numbers in 1-100 (inclusive) which are comprised entirely of odd digits.
If the "between" excludes 1 and 100, then there are 29 such numbers.
1000, 1020, 1040, 1060, 1080, and 1100
1111 is the only one.
If you think about the digits, you can rewrite them as ABBA, with A being one digit and B being another: A can be 1-9 and B can be 0-9. Since A has to be 1, B can be 0-9, leaving 10 palindromic numbers.
1100
One: 1001A palindrome reads the same forwards and backwards. Therefore for a 4 digit number:The first and last digits must be the sameThe middle two digits must be the sameStarting with 1000, the first palindrome will be 1001, then 1111, 1221, 1331, ...As it must be less than 1100, there is only one, 1001.