aha! : paul scott : mum’s the word

#2 96. MUM’S THE WORD

Hints and strategies

A palindrome is a word, a phrase, or a number which reads the same from left to right as it does from right to left.

For example, perhaps in 4004 BC (!) when Adam first met her man, he might have said “Madam, I’m Adam.” Again, there is the supposed saying of Napoleon: “Able was I, ere I saw Elba.” My favourite relates to a certain excavation in Central America: A man, a plan, a canal – Panama!

But enough of this! How many palindromic numbers are there between 0 and 1000 ?

HINT 1

The single digit numbers might be a special case?

HINT 2

Perhaps the two digit numbers could be treated separately as well?

SOLUTION

There are 9 palindromes between 0 and 10, another 9 between 10 and 100, and 90 between 100 and 1000 (having the form aba) giving a total of 108.

EXTENSIONS

We can obviously change the limits 0 and 1000 in the problem.

More interestingly, notice that the question asks about counting the numbers having a particular structure. This could be visible (e.g. how many numbers made up of even digits?) or mathematical (e.g. how many primes?).

#2 96. MUM’S THE WORD
			Hints and strategies Hint 1 Hint 2 Solution Extensions
*A palindrome* is a word, a phrase, or a number which reads the same from left to right as it does from right to left.** For example, perhaps in 4004 BC (!) when Adam first met her man, he might have said “Madam, I’m Adam.” Again, there is the supposed saying of Napoleon: “Able was I, ere I saw Elba.” My favourite relates to a certain excavation in Central America: A man, a plan, a canal – Panama! But enough of this! How many palindromic numbers are there between 0 and 1000 ?