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A palindrome number is the same either read from left to right or right to left, for example, ^@ 121. ^@ How many ^@ 5-^@digit palindrome numbers are there altogether^@?^@
Answer:
^@ 900 ^@
- We need to find the total number of ^@ 5-^@ digit palindrome numbers.
- ^@ 10 ^@ digits ^@(0, 1, 2, \ldots, 9)^@ can be used to fill in the places in the number.
The first digit cannot be zero in order to make it a ^@ 5 ^@ digit number.
Therefore, We have ^@ 9 ^@ choices for the first place.
For the ^@2^{ nd }^@ and the ^@3^{ rd }^@ place, we have ^@ 10 ^@ choices each. - For a ^@ 5-^@digit number to be a palindrome number the ^@1^{ st }^@ and the ^@5^{ th }^@ , the ^@2^{ nd }^@ and the ^@4^{ th }^@ digit of the number needs to be the same.
Therefore, the total number of ^@ 5 ^@ digit palindrome numbers ^@ = 9 \times 10 \times 10 = 900 ^@ - Hence, there are ^@ 900 ^@ ^@ \space 5-^@digit palindrome numbers altogether.
