A small coin nano-challenge

[Gerson W. Barbosa]

(03-23-2019 02:21 AM)Paul Dale Wrote:  You found a nickel (5c), thought you had a quarter (25c) at home but really had a dime (10c).

Any currency with three coins A, B and C such that (A + B) = 2(A + C) would work. I.e. A = B - 2C.

Coincidentally, the same choice of letters here, except mine were lower-case.

a: found coin
b: coin imagined to have at home
c: actual coin at home

{ a + b = x; a + c = x/2 }

{ a + b = x; 2a + 2c = x }

->

a + b = 2a + 2c

a = b - 2c

Considering current New Zealand set of coins is { 0.10, 0.20, 0,50, 1.00, 2.00 }, then { a = 1.00, b = 2.00, c = 0.50 } is the only solution for that set of coins.

{a = 0,05; b = 0,25; c = 0,10 } is a solution here (in Brazil) as well.