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Q: What three digit number whose digits are all odd and different has a sum of the three digits that is palindromic?

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a 8-digits palindromic number is a number consisting of a 4-digits number written and then written backward, i.e. 1234 4321 so there are as many palindromic 8-digits numbers as 4-digits numbers so from 1000 to 9999, so there are 8999 palindromic 8 digits number (I assumed that 00011000 is not to be considered as a valid 8 digit number)

585

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No.

To be a 3 digit palindromic number, it must be of the form aba.I assume that a 3 digit number must be at least 100 (so that 020 for example does not count as a 3 digit number):a can be any of the nine digits 1-9;for each of these b can be any of the ten digits 0-9Thus there are 9 x 10 = 90 three digit palindromic numbers.

1001 is the smallest 4 digit palindromic number.

There are 10 digits, but for a three digit number the first number cannot be a 0. Thus: there is a choice of 9 digits for the first (and last digit which must be the same), with 10 choices of digit for the second (middle) digit, making 9 × 10 = 90 such palindromic numbers.

102 is the smallest three digit number with different digits.

Let the first and third digits be equal. Choose any other number as the second digit. 202, 919, etc.

smallest 8 digit number with three different digits

9,999,876 is the greatest seven-digit number using four different digits.

9876 is the largest four digit number you can make if all the digits must be different.

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