Numismatic quiz question of the day. Well worth a look and guess

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We bought one of our magazines earlier this week and I like to do the quizzes within them.
Below is one that will interest all you people out there.
There is a list of numbers that have to be fitted into a crossword style grid, and the number that is left over, when correctly completed, is the answer to the posed question.

If you use only the standard UK coinage of 1p, 2p, 5p, 10p, 20p, 50p, £1 & £2, how many different ways are there to make exactly £2?

No cheating or using Google etc. Only guesses or actual working it out.

Answer will be posted tomorrow night around this time, so the whole world gets a chance.

Post your guesses and we will see who is closes. No prizes, just satisfaction of being closest.

Best of luck to you all. You will need it.
I'm just a collector of coins, not a slave to it, unless I am in a coin shop.
For all you banknote collectors. Link to my swap list.
https://colnect.com/en/banknotes/list/swap_list/COINMAN1
Goddamn maths! :(

Alright, just by using my fingers:

1. 1x £2
2. 2x £1
3. 4x 50p
4. 10x 20p
5. 20x 10p
6. 40x 5p
7. 100 x 2p
8. 200 x 1p

Eliminating the £2:
9. 1x £1, + 2x 50p
10. 1x £1, + 5x 20p
11. 1x £1, + 10x 10p
12. 1x £1, + 20x 5p
13. 1x £1, + 50x 2p
14. 1x £1, + 100x 1p

.....

<Gave up here because of traumatic flashbacks to my maths GCSE>
8192.
Catalogue administrator
Come on. Cass, Just a guess will suffice for now
I'm just a collector of coins, not a slave to it, unless I am in a coin shop.
For all you banknote collectors. Link to my swap list.
https://colnect.com/en/banknotes/list/swap_list/COINMAN1
Quote: "COINMAN1"​Come on. Cass, Just a guess will suffice for now
​Alright, I'll guess 1918.

@Jarek Was that a guess or did you go through with the maths?
2^13 x 3^2 - 46
Nope, I just counted my palm lines.
Catalogue administrator
73,682
The answer is 42. surprised no one else has thought of it.
Jamais l'or n'a perdu la plus petite occasion de se montrer stupide. -Balzac
42 must be correct...but what is the question? And don't forget your towel...
Sorry, off topic.

My guess is 256!
44 million
However many there are, most of the combinations you wouldn't want to be standing behind the person paying for a £2 cup of coffee with them.
What? Me Worry
Quote: "Idolenz"​2^13 x 3^2 - 46
Doesn't look like anyone else figured it out, what was your solution? I wasted about 5 minutes at work today throwing this together

#include<stdio.h>
main(){
int i,j,k,l,m,n,o,x=1;
for(i=0;i<201;i++){
for(j=0;j<101;j++){
for(k=0;k<41;k++){
for(l=0;l<21;l++){
for(m=0;m<11;m++){
for(n=0;n<5;n++){
for(o=0;o<3;o++){
if((i+(j*2)+(k*5)+(l*10)+(m*20)+(n*50)+(o*100))==200)x++;
}}}}}}}
printf("%d\n",x);
}
Quote: "sc.rednek"
Quote: "Idolenz"​2^13 x 3^2 - 46
​Doesn't look like anyone else figured it out, what was your solution? I wasted about 5 minutes at work today throwing this together

​#include<stdio.h>
​main(){
​int i,j,k,l,m,n,o,x=1;
​for(i=0;i<201;i++){
​for(j=0;j<101;j++){
​for(k=0;k<41;k++){
​for(l=0;l<21;l++){
​for(m=0;m<11;m++){
​for(n=0;n<5;n++){
​for(o=0;o<3;o++){
​if((i+(j*2)+(k*5)+(l*10)+(m*20)+(n*50)+(o*100))==200)x++;
​}}}}}}}
​printf("%dn",x);
​}
​I wrote almost the same program in basic. Then I couldn't figure out how to run it under windows 10.
So, how long does that C program take to run?
Quote: "phfoticus"​So, how long does that C program take to run?
​less than 2 seconds. It's only evaluating 2,884,061,565 possibilities.
I wonder how long those loops would take in something interpreted like Python, Ruby, Tcl, Perl, Javascript, PHP, etc. (one without JIT compilation)?
Quote: "phfoticus"​I wonder how long those loops would take in something interpreted like Python, Ruby, Tcl, Perl, Javascript, PHP, etc. (one without JIT compilation)?
​A bit longer, but probably still nothing unbearable. This was a 24 hour thread, so plenty of time to be patient... It could be optimized by doing partial sums at each level, and breaking that loop whenever it's greater than 200, a lot less total computations when you run it, but a lot more code to write. And I already had my answer so no reason to bother with that nonsense
I didn't write it myself I just remembered that somebody who likes these kind of riddles and likes to code send me this python script a while ago. I just modified it to the conditions of this quest.
Just a summation with arrays and took 1.8 sec for a complete run it seems.

def Anzahl(S, m, n ):

if (n == 0):
return 1

if (n < 0):
return 0;

if (m <=0 and n >= 1):
return 0

return Anzahl( S, m - 1, n ) + Anzahl( S, m, n-S[m-1] );

Muenzen = [1, 2, 5, 10 , 20, 50, 100, 200]
m = len(Muenzen)
print(Anzahl(arr, m, 200))
272
Quote: "JRo69"​272
​I cancel this answer
Ok, it's answer time. A little early, but its hot in my office, so I thought anyone who wanted to have a go, would have done so by now.
Attached are two photographs.
Left-the whole quiz, with numbers to left, crossed out if used and the crossword grid filled in.
Right-The list of numbers, clearly showing the one that has not been used, which is the answer.

I'm just a collector of coins, not a slave to it, unless I am in a coin shop.
For all you banknote collectors. Link to my swap list.
https://colnect.com/en/banknotes/list/swap_list/COINMAN1
The famous coin change problem ;)

https://www.geeksforgeeks.org/dynamic-programming-set-7-coin-change/
ROMA AETERNA
Hm so my friend didn't program it himself after all 8)
Well goddamn, that's a lot of combinations. Glad I quit where I did. :°
I guess 'plenty'is an answer that covers this problem well. I really do not like to get headach, doing maths, once
I am enjoying my favorit coin site in my small freetime:)...
...you can run,  but you can't hide...
Quote: "druzhynets"​The famous coin change problem ;)

https://www.geeksforgeeks.org/dynamic-programming-set-7-coin-change/
​There is a much more elegant algorithm. Here it is, in Python:
Quotetarget = 200
coins = [1, 2, 5, 10, 20, 50, 100, 200]
ways = [1] + [0]*target

for coin in coins:
for i in range(coin, target+1):
ways[i] += ways[i-coin]

print ("There are", ways[target], "ways to make", target)
[/i]


[i][i]The answer it produces is (runs in a fraction of a second): There are 73682 ways to make 200
[/i][/i]
HoH
I don't understand the posted scripts.
Idolenz: what is arr? It seems undefined.
Houseofham: initially ways is a list ("ways = [1] + [0]*target"), how can you add a number to it ("ways += ways[i-coin]")?
ūūūūū
it's the array so it should have been Muenzen in this case
Quote: "numinis"​I don't understand the posted scripts.
Idolenz: what is arr? It seems undefined.
Houseofham: initially ways is a list ("ways = [1] + [0]*target"), how can you add a number to it ("ways += ways[i-coin]")?
Argh!! Buggy forum ate some characters cause it thinks i in square brackets is bbcode for italic :(
ways[ i ] += ways[i-con]
HoH
That is a brain fryer.

How about for spice, we assume its 1984 and we also have the ½p coin, what would that take it up to?
:8D
I love coins. Especially silver, gold and anything really old.
Member of the Royal Numismatic Society of New Zealand and the Auckland Numismatic Society
2886726
Quote: "Moneytane"​That is a brain fryer.

​How about for spice, we assume its 1984 and we also have the ½p coin, what would that take it up to?
:8D
​You want spice? I'll give you spice.

Farthing, halfpenny, penny, twopence, threepence, groat, sixpence, shilling, florin, half crown, crown, sovereign.

Make £2 from that. X-D

If anyone's complaining I'll throw in the 1 1/2 pence in there.
光復香港 時代革命
五大訴求 缺一不可
Liberate Hong Kong, Revolution of our times

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