A small coin nano-challenge

[brickviking]

I saw Valentin's #minichallenge, and my eyes glazed over after I saw the first question. So I thought I'd come up with my own nano-challenge after an event that actually happened to me.

Caveat: I haven't managed to "prove" this one myself, it seems I left school with passable maths that have degraded since for lack of use. It's also dependent upon whose currency you choose to implement this in.

I have a single coin at home. I went out one day, and found another coin. "Ooo goodie", I thought, "I've got x money now." When I got home, I found I had only ended up with half the money I thought I had.

What two coins would make this true, and for whose currencies is it currently valid? In my case, only one set of coins meets the stated properties. I'm also talking only about coins in current circulation, not commemorative coins.

(Post 328)

[StephenG1CMZ]

One explanation might be that the currency has been revalued.
If you have a £1 coin and get a second £1 coin, you might think you have £2, but the uncertainty caused by Brexit might mean the £2 is only worth £1 by tomorrow.
I cannot think of an alternative explanation (apart from mistaking a 50p and a 10p coin because they are a similar size).
But I suspect there is another explanation.

[Gerson W. Barbosa]

(03-22-2019 09:57 PM)brickviking Wrote:  I saw Valentin's #minichallenge, and my eyes glazed over after I saw the first question. So I thought I'd come up with my own nano-challenge after an event that actually happened to me.

Caveat: I haven't managed to "prove" this one myself, it seems I left school with passable maths that have degraded since for lack of use. It's also dependent upon whose currency you choose to implement this in.

I have a single coin at home. I went out one day, and found another coin. "Ooo goodie", I thought, "I've got x money now." When I got home, I found I had only ended up with half the money I thought I had.

What two coins would make this true, and for whose currencies is it currently valid? In my case, only one set of coins meets the stated properties. I'm also talking only about coins in current circulation, not commemorative coins.

(Post 328)

You had 50c at home (not $2), which added to the $1 you found made $1.50.

[Paul Dale]

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.

Australia has 10c, 50c, 20c and 5c, 20c, 10c as do many other countries, which meet these restrictions. We also have 50c, $2, $1 as Gerson mentioned. Once a $5 coin is introduced, we'll have $1, $5 and $2 as a fourth. There is no talk of replacing the $5 note with a coin, so it is a way off.

Although not used anymore, Australia still accepts older and pre decimalisation coins as legal tender, giving more possibilities: 1c, 5c, 2c or penny (1d), threepenny (3d), penny or shilling (1s), crown (5s) and florin (2s). Now things get interesting, the pre-decimal coins have conversions to decimal, sixpence being five cents. This adds mixtures: shilling, 50c, 20c and 50c, florin, shilling and penny (converted to 1c), sixpenny (converted to 5c), 2c and many more combinations. Unfortunately, we missed out on all the myriad small denominations. Pre-federation coins are also nearly all legal tender still which I suspect introduces even more possibilities. Nobody in their right mind would spend pre-decimal currency. It's worth a lot more to collectors.

Pauli

[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.

[Paul Dale]

I didn't realise that NZ had drop the 5c.

There was talk about it here a couple of years back.


It would be interesting to see what combinations of old English coins would work. There were plenty of coins spaced apart by a factor of two (found 2, thought 4 but had 1): quarter farthing, half farthing, farthing, halfpenny, penny, twopenny, groat and the threepenny, sixpence, shilling, florin. The A groat (4), penny (1) and sixpence (6) works too with different numerical ratios. Any chance of one involving the fivepenny (pronounced fip-enny, one of the few words with a silent V)?


Pauli

[brickviking]

(03-23-2019 04:05 AM)Gerson W. Barbosa Wrote:  

(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.

Just to set the record straight, I am from New Zealand, and there is (as I found) two sets of coins (and not just the one I thought of) that match that. I found a ten cent piece. I thought I had a fifty cent piece at home, but I only had twenty cents. That (of course) made thirty cents, not sixty cents. Sigh.

Inaccurate guess: a=0.50, b=0.10, c=0.60
Actual result: a=0.20, b=0.10, c=0.30 (a is coin at home, b is coin I found, c is total).

Still, thanks for the illumination, everyone. Does anyone know of a currency where there's only one solution?

(Post 329)

[Gerson W. Barbosa]

(03-23-2019 10:32 AM)brickviking Wrote:  Does anyone know of a currency where there's only one solution?

The Swedish crown, for instance:

{ 1 kr, 2 kr, 5 kr, 10 kr } -> a = 1 kr; b = 5 kr; c = 2 kr.

I should have written a small program that ran through all possibilities, as I’ve done on the HP-75C. BTW, here we have two solutions as well: { 0,05; 0,25; 0;10 } and { 0,50; 1,00; 0,25 }, from the coin set { 0,01; 0,05; 0,10; 0,25; 0,50; 1,00 } (The R$ 0,01 copper coin apparently doesn’t circulate anymore, but has been taken into account).