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# How many palindromic 4 digit numbers are there less than 5000?

Updated: 9/19/2023

Wiki User

13y ago

40. Excluding numbers starting with 0.

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13y ago

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Q: How many palindromic 4 digit numbers are there less than 5000?
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While I'm tempted to tell you to do your own homework, this is intriguing enough that I'm willing to spend some time helping you to work it out.First: by four digit palindromes that means numbers of the form ABBA.A is constrained by "less than 5000". A can only be 0, 1, 2, 3, or 4, because otherwise ABBA would be greater than 5000 (the lowest possible ABBA number where A is 5 or greater is 5005 ... which is over 5000).A is further constrained by "4 digit". It can't be 0, because by convention we don't write leading zeroes and then ABBA would only be a three digit number.So A can be 1, 2, 3, or 4 (4 distinct possibilities).There are no constraints on B. It can be any digit (including 0), which means there are 10 distinct possibilities.Since once we specify both A and B we're done, that means there are (4 possibilities for A) x (10 possibilities for B) = 40 four-digit palindromes less than 5000.

### Which is the tens digit is less than the ones digit?

Not sure what you're asking, but here are some examples of numbers that have a tens digit less than the ones digit: 13, 205, 1367, 29.632

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### What is the ones digit in the product of all the prime numbers less than 2012?

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