In the land of Trioscentos, the system of currency, the trient is remarkably different: understandable in the light that they hold the number three sacred. The denominations available are: \(1,3,9,27...\) i.e. the whole number powers of \(3\). A rule forbids a particular denomination to be used more than once in a transaction. So, if somebody notices you carrying/paying with more than one coin of a particular denomination, you are sentenced to death. So, to purchase an article priced \(6\) trients, you do not pay two \(3\) trient coins (punishable!), but pay a \(9\) trient coin and take back \(3\) trient coin from the seller. Note that neither you nor the seller used any currency twice!
It is easy to observe that all articles can be bought however. But, is the way always unique? Let \(Y\) denote the sum of prices of objects less than \(100\) that may be bought in multiple ways of transaction. Find \(Y\).