Coin combinations

[LPP1999]

How many different ways exist to make a total of seventeen pence?

[Postdog]

Lots - just gone mad trying to work it out!!

BTW I answered so I could find the question again when someone does say

[fordward]

6 !!

[Postdog]

It's more than 6 just doing a combo of 1p and 2p, then you have your 5p and 10p's to account for

[vulcan]

11.[I think]

[Jumbuck]

I make it 27 different ways:

16x1p / 14x1p+1x2p / 12x1p+2x2p / 10x1p+3x2p / 8x1p+4x2p / 6x1p+5x2p / 4x1p+6x2p / 2x1p+7x2p / 8x2p

1x5p+...11x1p / 9x1p+1x2p / 7x1p+2x2p / 5x1p+3x2p / 3x1p+4x2p / 1x1p+5x2p

2x5p+...7x1p / 5x1p+1x2p / 3x1p+2x2 p/ 1x1p+3x2p

3x5p+ ...2x1p / 1x2p

1x5p+1x10p+...2x1p / 1x2p

1x10p+...7x1p / 5x1p+1x2p / 3x1p+2x2p / 1x1p+3x2p

[Jumbuck]

made a mistake, for some reason took 16p instead of 17s so...

1st row: add 1p to each combination - still 9 combos

2nd row: add 1p to each combination - adds one extra combo

=> grand total = 28

[dr b]

I think it's 102 (assuming you have 10p, 5p, 2p and 1p coins)

Logic: using a 10p coin there are 6 ways:

10-5-2
10-5-1-1
10-2-2-2-1
10-2-2-1-1-1
10-2-1-1-1-1-1
10-1-1-1-1-1-1-1

Now, how many ways can you make 10p, using a 5 p coin? Answer: 4
5-5
5-2-2-1
5-2-1-1-1
5-1-1-1-1-1

For each of these 4 ways there are 6 more ways to get to 17 (see above) so that's 24 more in total.

Finally, how may ways to make 5p? Answer: 3
2-2-1
2-1-1-1
1-1-1-1-1

For each of these 3 ways there are 24 ways to get to 17p (see above) so that's 72 more

72+24+6 = 102.

[fordward]

quite right forgot to do all the 1ps think i should go to bed!

[Postdog]

Should have read my first answer....

[vulcan]

I shouldn't have answered at all ! :-)

[Jumbuck]

dr b the problem with your reckoning is that it doesn't take into account the interchangeability of individual coins of the same denimination

e.g you are counting (2-1-1-1) + (2-1-1-1) + (2-1-1-1) as being different from (2-2-1) + (2-1-1-1) + (1-1-1-1-1)
whereas they are both 9x1p + 3x2p

[fordward]

wonder if its an age thing vulcan

[vulcan]

I fear you're right, fordward, old age is like being punished for a crime you didn't commit.!

[Jumbuck]

you old codgers, you're wrong if you reckon that everyone else on this thread is a youngster

[dr b]

Jumbuck, too true, although I like to think of this as a 'salient feature' of my solution rather than a 'problem'. If the order of the coins doesn't matter I make it 26 combos, so we still get to disagree!

[dr b]

whoops, no, 27 ways. So we concur.

[Jumbuck]

not quite dr b I upgraded to 28 because (for some reason) I started with 16p, so the updated version is

17x1p / 15x1p+1x2p / 13x1p+2x2p / 11x1p+3x2p / 9x1p+4x2p / 7x1p+5x2p / 5x1p+6x2p / 3x1p+7x2p / 1x1p+8x2p = 9 combos

1x5p+...12x1p / 10x1p+1x2p / 8x1p+2x2p / 6x1p+3x2p / 4x1p+4x2p / 2x1p+5x2p / 6x2p = 7 combos

2x5p+...7x1p / 5x1p+1x2p / 3x1p+2x2 p/ 1x1p+3x2p = 4 combos

3x5p+ ...2x1p / 1x2p = 2 combos

1x5p+1x10p+...2x1p / 1x2p = 2 combos

1x10p+...7x1p / 5x1p+1x2p / 3x1p+2x2p / 1x1p+3x2p = 4 combos

9+7+4+2+2+4 = 28

[dr b]

yes, I agree.

[fordward]

well thats nice!