A logical approach?

I am doing a puzzle (from loooong ago, I got a little behind...) and, while I can solve it using a bit of educated trial and error, the mathematician in me is (almost) sure there must be a nice logical way this can be approached, perhaps involving a forumla.

£20.32 is in a tin.  There are 4 denominations of coin (£1 and less) and the same number of each coin.  How many coins and which?

As I say, I can solve it, but it was a bit too random for me and I want a nice approach for next time.

Best I can do is (xa)+(xb)+(xc)+(xd)=£20.32

Ooooh, so that could be written as x(a+b+c+d)=£20.32, which is a little clearer...  But too many variables!

Comments

Try this approach

GW | | Permalink

Work in pence.

Factorise 2,032

2,032 is  2x2x2x2x127

Given the available denominations are 1,2,5,10,20,50,100 find which four add up to 127

Answer 100+20+5+2

Solution to problem there are 16 (2x2x2x2) each of £1, 20p, 5p and 2p coins

Try this approach

GW | | Permalink

Work in pence.

Factorise 2,032

2,032 is  2x2x2x2x127

Given the available denominations are 1,2,5,10,20,50,100 find which four add up to 127

Answer 100+20+5+2

Solution to problem there are 16 (2x2x2x2) each of £1, 20p, 5p and 2p coins

Try this approach

GW | | Permalink

Work in pence.

Factorise 2,032

2,032 is  2x2x2x2x127

Given the available denominations are 1,2,5,10,20,50,100 find which four add up to 127

Answer 100+20+5+2

Solution to problem there are 16 (2x2x2x2) each of £1, 20p, 5p and 2p coins

Try this approach

GW | | Permalink

Work in pence.

Factorise 2,032

2,032 is  2x2x2x2x127

Given the available denominations are 1,2,5,10,20,50,100 find which four add up to 127

Answer 100+20+5+2

Solution to problem there are 16 (2x2x2x2) each of £1, 20p, 5p and 2p coins

Try this approach

GW | | Permalink

Work in pence.

Factorise 2,032

2,032 is  2x2x2x2x127

Given the available denominations are 1,2,5,10,20,50,100 find which four add up to 127

Answer 100+20+5+2

Solution to problem there are 16 (2x2x2x2) each of £1, 20p, 5p and 2p coins

Constantly Confused's picture

Gosh

Constantly Confused | | Permalink

Not only have you taught me a new mathematical approach (for which I am eternally grateful), you've repeated it so many times it will now be burned into my retina! ;)

mwngiol's picture

Dumber than Dumby McDumb from Dumbarton

mwngiol | | Permalink

As someone to whom anything more advanced than 2 x 2 is akin to rocket science, how do you work out the 2,032 is  2x2x2x2x127 bit?

Its all down to prime numbers

GW | | Permalink

mwngiol wrote:

As someone to whom anything more advanced than 2 x 2 is akin to rocket science, how do you work out the 2,032 is  2x2x2x2x127 bit?

 

You just need to divide by prime numbers (as you may remember from school, you can't divide a prime number by another number without getting a fraction so the sequence of prime numbers starts 2, 3, 5, 7, 11, 13, 17 etc.ignoring the debate about whether 1 is a prime number!)

as 2,032 is even it can be divided by 2

 

So 2,032 = 1,016x2

keep repeating the process:

=508x2x2

=254x2x2x2

=127x2x2x2x2

and 127 is a prime number so you can't go any further.

Now hopefully the computer won't play silly games again and this will only be posted once 

mwngiol's picture

Many thanks!

mwngiol | | Permalink

One of the most common things people say to me when I say I work in accountancy is "you must be good at maths then". But actually I'm quite the opposite!

And judging from other people I've talked to in the industry, I'm far from being alone. Maybe this shows how little understanding people have of what we do.

Democratus's picture

Good at maths; yeah, that's not right at all

Democratus | | Permalink

I often surprise people by telling them that you don't have to be good at maths to be an accountant, just be able to add, subtract, multiply and divide. A bit of statistics is good.

I hate when i am brought in a mathematical puzzle by someone to solve just because i am a bean counter.

I am fascinated by the subject but it's way too difficult for my mind to encompass. I have a just scraped pass at A level maths, though that was back in the day when exams were real exams and teachers were real teachers. Just after slide rules but before calculators for anyone wishing to guess.

i wonder, what did i do with my slide rule?..............ambles off confusedly mumbling to self ......

.......... .... .. .   .  .

Monsoon's picture

Uh?

Monsoon | | Permalink

Democratus wrote:

I often surprise people by telling them that you don't have to be good at maths to be an accountant, just be able to add, subtract, multiply and divide. A bit of statistics is good.

I'm with Democratus. My brain hurts. I got an A for GCSE maths, but I wouldn't have a clue how to solve the above with mathematical logic. Ugh!

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