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 2011-12-13 22:49:22