The government of Nova Mareterrania requires that various legal documents have stamps attached to
them so that the government can derive revenue from them. In terms of recent legislation, each class
of document is limited in the number of stamps that may be attached to it. The government wishes to
know how many different stamps, and of what values, they need to print to allow the widest choice of
values to be made up under these conditions. Stamps are always valued in units of $1.
This has been analysed by government mathematicians who have derived a formula for n(h, k), where
h is the number of stamps that may be attached to a document, k is the number of denominations of
stamps available, and n is the largest attainable value in a continuous sequence starting from $1. For
instance, if h = 3, k = 2 and the denominations are $1 and $4, we can make all the values from $1 to
$6 (as well as $8, $9 and $12). However with the same values of h and k, but using $1 and $3 stamps
we can make all the values from $1 to $7 (as well as $9). This is maximal, so n(3, 2) = 7.
Unfortunately the formula relating n(h, k) to h, k and the values of the stamps has been lost — it
was published in one of the government reports but no-one can remember which one, and of the three
researchers who started to search for the formula, two died of boredom and the third took a job as a
lighthouse keeper because it provided more social stimulation.