An integer n is called 'paladin' if the number of positive divisors of n is equal to the number of digits of n.

a) Determine all three-digit 'paladin' numbers.

b) Determine a 'paladin' number with four digits that is less than 1300.

[OPM 2012 Level Beta Paper1 Q2][Original in Portuguese. My translation into English.]

[OPM = Olimpiada Paulista de Matematica, Brazil]

The same question is repeated in the Gamma Level paper (borderline middle/upper secondary) but with a harder part (b).

b2) Determine a 'paladin' number with six digits that is less than 110000.

[OPM 2012 Level Gamma Paper 1 Q1]

**Feel free to comment, ask questions and even check your answer in the comments box below powered by**~~Disqus~~ Google+.

}

This space is here to avoid seeing the answers before trying the problem!

}

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.}

This space is here to avoid seeing the answers before trying the problem!

}

If you enjoy using this website then please consider making a donation - every little helps :-)

You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.

Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..

You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.