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8 March, 00:06

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?

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  1. 8 March, 00:25
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    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.
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