Numbers such as 252, 3663, and 50405 are palindromes because the number reads the same forward as backward. In how many palindromes between 10 and 10000 does the digit 1 appear at least once?

The answer is 39.

Step-by-step explanation:

I will divide the range into 5 division to count palindromes more easy.

From 10 to 100:

11

There are only 1 number exist that at least the digit 1 appears once.

From 100 to 1000:

Section 1:

_1_ (e. g. 212)

There are be 9 numbers exist that at least the digit 1 appears once from above number structure.

Section 2:

1_1 (e. g. 121)

There are be 10 numbers exist that at least the digit 1 appears once from above number structure.

From 1000 to 10000:

Section 1:

1__1 (e. g. 1221)

There are be 10 numbers exist that at least the digit 1 appears once from above number structure.

Section 2:

_11_ (e. g. 2112)

There are be 9 numbers exist that at least the digit 1 appears once from above number structure.