To buy a certain gadget you need at least four US coins,- two similar gadgets require no less than six coins while for a purchase of three only two coins are needed.
What minimal price of the said item fits the description above?
Rem: The coins denominations are 1,5,10,25,50,100 cents .
Consider first buying 3 items with two coins. The two coins must sum to a multiple of 3, so the three must cost either 6, 15, 30, 51, 60, 75, 105 or 150 cents.
That makes one gadget either 2,5,10,17,20,25,35 or 50 cents.
Only 17 cents requires more than two coins, so that is our solution. It is not only minimal, it is unique.
Just as a check, two gadgets costs 34 cents, which requires at least 6 coins.