Puzzle of the day

Just finished this puzzle in a magazine.
If the Americans use each of their coins from 1 cent to 1 dollar, there are 293 different ways of making 1 dollar. (Multiples of the same face value coin is allowed)
Question?
Using the same principle with UK coins, how many different ways are there of making 1 pound?
Answer tomorrow unless requested to give a bit longer.

if we are talking about the decimal pound:
1000111010011₂

I would like to know the answer when we use the old pound with the old coins. There are just to many denominations and I get a buffer overflow no time to fix that.

It is just the decimal currency as far as I can tell.

A ridiculous amount, having the 1 and 2 penny coins rather than just the 1 cent coin would really boost it.

Quote: "Idolenz"​if we are talking about the decimal pound:
​1000111010011₂
​
​

​My memories of the combinatorics courses are very vague. May you detail ?

https://en.numista.com/forum/topic72405.html
just slightly different parameters

Answer time.
According to the magazine, the answer is 4563

Quote: "Idolenz"​I would like to know the answer when we use the old pound with the old coins. There are just to many denominations and I get a buffer overflow no time to fix that.
​
​

​16371.
(I assume that the coins used are: 1 farthing, 4 farthings aka penny, 48 farthings aka shilling, 96 farthings aka florin, 240 farthings aka crown, 960 farthings aka sovereign.)

Update: I forgot 1/2 penny, 3 pence, 6 pence and half crown. So the sequence is 1, 2, 4, 12, 24, 48, 96, 120, 240, 960 and the number of combinations is larger.

No, I meant all of them from 1/4 Farthing up to the guineas and sovereign, otherwise I wouldn't have had the problem with the overflow (I work with 64 bit so it should be bigger than 9.223.372.036.854.775.807)

With Elizabeth II predecimal set (10 coins) I got 382141950.
UPD: perhaps it is wrong to count sovereigns and crowns as they didn't circulate?
What was the maximum number of pre-decimal coins that really circulated at some time?

If you are going to use pre-decimal coinage, then you must add in the 1/4 farthing, 1/3 farthing and the 1/2 farthing.

That means there are 3,840 1/4 farthings in a pound and so on.
Stopping now as my brain is aching already

Quote: "Idolenz"​https://en.numista.com/forum/topic72405.html
​just slightly different parameters

​I understand it's more algoritmic than combinatorics
But why in base 2

The same reason I used the number representation format in the old thread, so that you don't see the solution right away ... maybe someone else wanted to do their own math.

I've tried with excel, but it seems there is not enough lines

Quote: "Idolenz"​No, I meant all of them from 1/4 Farthing up to the guineas and sovereign, otherwise I wouldn't have had the problem with the overflow (I work with 64 bit so it should be bigger than 9.223.372.036.854.775.807)

​Can you provide a list of the denominations you used?

The version I originally tried was [3, 4, 6, 12, 24, 48, 72, 96, 144, 192, 288, 576, 1152, 1440, 2304, 2880, 5760, 11520] (in units of 1/12 farthing), i.e. 1/4 farthing, 1/3 farthing, 1/2 farthing, farthing, halfpenny, penny, 1 1/2 d, 2d, 3d, 4d, 6d, shilling, florin, half crown, double florin, crown, half sovereign, sovereign. The result was about 1/6 of your upper bound.

Now that I've checked Numista's list of UK coins, I found that this list should also include 1/4 guinea, 1/3 guinea, and 1/2 guinea, which would be 3024, 4032, and 6048, respectively. (The full guinea is too large to show up.) This still does not push the count above 20% of your bound.

I suspect that you included the English 3 farthings, which is honestly cheating. They hadn't made those since 1577.

Most likely some rounding errors or what not ... I'm no programming aficionado I just know the basics and also didn't want to invest more time to correct the mistake.

It seems I didn't use more than you:
¼, ⅓, ½, 1 Farthing; ½, 1, 2, 3, 4, 6 Pence; 1, 2 Shilling; ½, 1 Crown; ¼, ⅓, ½ Guinea; 1 Sovereign (18 different denominations)

Quote: "Idolenz"​Most likely some rounding errors or what not ... I'm no programming aficionado I just know the basics and also didn't want to invest more time to correct the mistake.
​
​It seems I didn't use more than you:
​¼, ⅓, ½, 1 Farthing; ½, 1, 2, 3, 4, 6 Pence; 1, 2 Shilling; ½, 1 Crown; ¼, ⅓, ½ Guinea; 1 Sovereign (18 different denominations)

​I would definitely have added at least the double florin (4 shillings) and ½ sovereign to this list. I'm less sure whether the 1½ pence qualifies, but even including it I get a result, as mentioned, somewhat less than your boundary figure. (Without it, the result goes down to under 2% of your figure.)

It's possible that you converted the farthing fractions incorrectly in some way. It's also possible that it was me who messed up somehow.