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 .
Excluding the minimal price requirement, and permitting US currency [paper money], the two coins required in the purchase of three gadgets [with X being an integral dollar amount] are:
(A) a half dollar and a cent for a single gadget sold at $X.17;
(B) two cents for a single gadget sold at $X.34; and
(C) a dime and a cent for a single gadget sold at $X.37
GADGETS COINS
(A) 1 4 : (1X)$ + 10+5+1+1 = $X.17
2 6 : (2X)$ + 25+5+1+1+1+1 = $(2X).34
3 2 : (3X)$ + 50+1 = $(3X).51
(B) 1 6 : (1X)$ + 25+5+1+1+1+1 = $X.34
2 6 : (2X)$ + 50+10+5+1+1+1 = $(2X).68
3 2 : (3X+1)$ + 1+1 = $(3X+1).02
(C) 1 4 : (1X)$ + 25+10+1+1 = $X.37
2 7 : (2X)$ + 50+10+10+1+1+1+1 = $(2X).74
3 2 : (3X+1)$ + 10+1 = $(3X+1).11
Ergo, with the minimal price requirement, the price would be $0.17.

Posted by Dej Mar
on 20111213 22:49:22 