In A few coins, we learned about Levikland, in which the currency is perplexii. The coin values are 1, 2, 5, 10, 20, 50, and 100 perplexii.

How many perplexii can you have and still not be able to make change for a 100 perplexii coin?

The question specifically asks 'How many perplexii can you have and still not be able to make change for a 100 perplexii coin?'

So, the way I'm seeing the question is this:  I imagine myself to be in Levikland, and one of the inhabitants approaches me proffering a 100 perplexii coin and asking 'Can you give me change for this?'  Obviously I could have a pocket full of 100 perplexii coins and still not be able to satisfy this person!  He doesn't simply want to trade coins of the same denomination with me - he wants me to give him a collection of coins of smaller denomination which total 100 perplexii.

So, I would argue that I could have any non-negative integral number of perplexii and still be unable to make change for a 100 perplexii coin!  (I can have in my pocket any number of 100p coins and any number from 0 to 99 inclusive of 1p coins - in this way I can indeed have any integral amount of perplexii from 0 up)

Perhaps I am splitting hairs here?  I would imagine that if this was the intended solution that the problem would probably have been posted in the category 'Tricks'.  Comments?

-John

Posted by John Reid on 2005-05-12 14:41:54