In a foreign country, when you pay A, B, and D coins for a purchase, you receive C, E, E, and F as change.

Question

When you pay D, D, A, A, and F for the same purchase, you receive E and C as change. You suspect that the coins have values equivalent to 1, 5, 10, 25, 50 cents and $1. But which is which? (or, what is the purchase price, etc.)?

Answer 1

Strategy: Work upwards in value, with trial and error.

Tactics: E and C appear to be smaller value, since you get them repetitively as change. So tentatively assign them to 1 and 5 cents. A can't be all that valuable, since two payed only gets you a single E and C as change. So assign that as 10 cents, tentatively. B seems quite valuable, since one of it paid shakes the money tree for change! So assign it as $1, temporarily. Then with A, B, C, D, E, and F at 10, 100, 5, 25, 1, 50 respectively, $1.35 paid gets you 5 + 1 + 1 + 50 = $0.57 change; the item cost $0.78. Check this against the second purchase: 25 + 25 + 10 + 10 + 50 = $1.20, with 6 cents change, item cost $1.14, does not check!

Bopping A up to 25 cents, and trying 25, 100, 5, 10, 1, 50: $1.35 paid, $0.57 change, purchase was $0.78; versus $1.20 paid, 6 cents change, cost $1.14, still does not check, no closer to solution.

So need to pay more on the first purchase: try 25, 100, 1, 50, 5, 10 : now $1.75 tendered, $0.21 change, purchase $1.54, vs. $1.60 tendered, 6 cents change, $1.54 purchase. Matches, that's good enough to “take to the bank”, so to speak!