Cupidinous Convivial Country

Logic Level 4

The currency of United Kingdom (UK) is called pounds (£), with 1 pound equivalent to 100 pennies (\(p\)). The denomination of the coins are: \(1p, 2p, 5p, 10p, 20p, 50p\). The minimum coins I needed to carry so that I could make any value from \(1p\) to \(99p\) is 8.

Now suppose the currency of a fictitous country next to the UK is called dounds, with 1 dound is equivalent to 100 antidisestablishmentarianism (\(a\)). This country has a ridiculous denomination of coins, namely: \( 1a, 3a, 13a, 53a, 93a\). What is the minimum number of coins I needed to carry so that I could make any value from \(1a\) to \(99a\)?

Image Credit: Wikimedia British coinage reverse designs 2015.
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