Using only 5s and 9s (any number of each), what is the largest total that cannot be made?

combinatorics/coinage/largest.unreachable New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Using only 5s and 9s (any number of each), what is the largest total
that cannot be made?  In general, using m's and n's?
[ Editor: problem statement reconstructed from the reply; the original
question by Eric Angelini is not in the collected postings. ]

Show solution

In article <keynews.tv-1305971627490001@bru-usr1-18.sky.be>, Eric
Angelini <keynews.tv@skynet.be> writes
> if i understand you well, there will always be an unreachable
>value by the mean of adding 5's and 9's?

If I have understood you, the answer you are looking for is 31.  The
general formula is mn-m-n.

-- Nick Wedd <nick@maproom.demon.co.uk>

[ Editor: 5*9 - 5 - 9 = 31.  The formula needs m and n to have no
common factor: with 4s and 6s no odd total can be made. ]