How many beans are in this tin?
 

I was recently asked the question Can you tell me exactly how many beans there are in a tin?

The tin I have is 398ml of "Heinz original Beans in Tomato Sauce". Photos of the actual can and ingredient list are attached.

So how many beans are in the tin (please show all work for your calculations!)??

I'll open it and count the beans later this week. No prize (unless you want me to mail you the beans) but it's a fun problem, I'm on vacation and a bottle of Cruzan is staring invitingly at me :thumbup:

Re: How many beans are in this tin?
 

My guess is 381.454 beans.

The method I chose was to convert a bean into a cuboid measuring 13mm x 8mm x 8mm. The measurements were based on a guess at average bean size plus space it occupied with fluid around it (as well as any free "air" space in the can). 13x8x8mm sounds big but I shook the can and it sounds like there's a lot of fluid and free space in there (so I added a bit extra to my guesstimated average bean size to compensate).

I then divided this bean cuboid into a cuboid version of the can.

The can has a height of approximately 105mm and a radius of about 35mm. To convert the can into a cuboid I used it's original height but for length and width I used 2*radius*0.7854. The magic number 0.7854 is the ratio of an area of a circle to the area of a square it will fit exactly in.

Re: How many beans are in this tin?
 

ehem, you've nothing better to do with vacation time?? That's sad. Unless of course you're a maths freak in which case, enjoy.

Re: How many beans are in this tin?
 

You're right, of course. I've already done my math bit though so will switch attention to other, regular, forms of relaxation (which will include thinking up clever, creative ways of influencing a seven year old to count the beans for me)..

Re: How many beans are in this tin?
 

Oh, dear, not very sophisticated.

A baked bean is a prolate spheroid with a minor diameter of about 0.35 cm and a major diameter of ~0.7 cm. The volume of a bean is therefore 1/6(pi)0.3x0.3x0.6 cc = 0.0449 cc.

The tin has a volume of 398 cc, of which I guestimate 28 cc is occupied by sauce and perhaps a headspace of 10 cc is empty.

Thus the number of beans is precisely 360/0.0449 but since only quantized states are allowed, this is 8018.

Re: How many beans are in this tin?
 

Utter tosh - Tosh.

My theory is that that variety has more sauce and fewer beans than most so I would say that more than a tenth of the volume is sauce and space.

The number what I have chosen is.........278

Re: How many beans are in this tin?
 

Those Canadian beans in Tomaida sauce is bigger than what i is remembering in the UK

For that reason i go for 317 beans.:blink:

Re: How many beans are in this tin?
 

See, as soon as I mentioned my short-cut cuboid method to the OH, she gave me that look [that I was just being silly]. So I knew straight away that solving this problem based on volumes is probably not the easiest way of arriving at an accurate answer.

I'm sticking with my guess though (and will post up OH's theorem when she's finished toying with my comparatively-feeble mind)..

Re: How many beans are in this tin?
 

I've just finished dinner (not baked beans, honest) and I think my result must be too high. I think I need to take account of the Coriolis force ;), so I'll reduce it by half : 4009.

Re: How many beans are in this tin?
 

Are you channelling immichaelcaine?

Re: How many beans are in this tin?
 

You haven't even considered the Murmansk effect have you?

Re: How many beans are in this tin?
 

Frozen beans? No thank you.

Re: How many beans are in this tin?
 

The picture of the front label on the can (attachment, post #1) I think shows a top layer of no more than 40 beans. Are you suggesting there are 100 layers of beans in that white bowl? I'm assuming not, of course, that the "4009." at the end of your sentence was a typo and you meant "400.9"??

Re: How many beans are in this tin?
 

When I worked at Heinz I used to go boozing occassionally with a couple of workmates, we used to tease any girls we picked up by telling them that one of us counted the beans in, the other poured the sauce in and the last one put the lid on.

No-one ever believed us :o

We said 248, wrong of course.

Weigh the tin, then weigh a bean, then weigh an empty tin, then do the math(s) :thumbsup:

Re: How many beans are in this tin?
 

All very well, but I don't (as usual) have a tin of beans in the house; nor do I have a chemical balance at home.

Perhaps I'll perform your experiment tomorrow at work, that is to say, order a graduate student to do it, (his reward would be a can of beans), but also perhaps not.

Re: How many beans are in this tin?
 

Yes, by God. That's exactly what I'm suggesting!!!!!

Just you wait until your 7 yr old does the dirty deed.

And you can't have 0.9 of a bean in my world. Oh, no.

Re: How many beans are in this tin?
 

The bean tins I have just emptied across the floor in this hotel room held 405, 421, 410, 417 (and a squished bit), 435 and 433 beans respectively. You'll be using metrical beans so they won't fit the tin properly, nonetheless, based on this analysis, I reckon 425.

Re: How many beans are in this tin?
 

A squished bit!!!??? You mean beans violate quantum theory???

Re: How many beans are in this tin?
 

I , of course , as a very cleverperson have spent the last few hours embroiled in 3rd order differential equations combined with advance Fourier analysis to come up with an answer accurate to 27 decimal places ( quantized states only , tosh!)

However it only works for beans in a vacuum , sorry !

Re: How many beans are in this tin?
 

They were on the floor, so it's string theory

Re: How many beans are in this tin?
 

I am saddened to inform BE that the standard UK tin of Heinz Baked Beans (415g) contain a mere 51% beans (presumably by mass). Thus a UK tin contains only ~212g of beans, assuming a similar state of affairs in Canada and also assuming the average bean weighs ~1g. Then there would be 212 beans.

This seems a little bit of an underestimate though, and my slices of toast coated in hundreds of the little things seem to attest to a slightly higher number.

Re: How many beans are in this tin?
 

I have a tin of Schrodinger's Beans, which has 450 beans in it, and no beans in it.

I don't know how much toast to make.

Re: How many beans are in this tin?
 

Does a partial bean count as a "bean" in this context, or are we to total up all the half beans and give a grand total as it were;) (which is going to make totaling them up harder for the bean counter!)

Enquiring minds need to know.

As usual google has the answer... 375 beany bites, or if you prefer method B 355 total beans, give or take.

Or 557.

Re: How many beans are in this tin?
 

4 slices. You can always eat it without the beans;)

Re: How many beans are in this tin?
 

Damn, I was just going to make a Schrodingers cat funny and Jings beat me to it.:frown:

There are of course an infinite number of beans in an infinite number of dimensions. Pray that your can doesn't contain an inter-dimensional tear otherwise there is going to be one helluva mess when you open it.

On another note. Baked Beans win my prize of the most revolting food in the world. You couldn't pay me to eat them.

Re: How many beans are in this tin?
 

305 beans.

Re: How many beans are in this tin?
 

A more pertinent question would be, "How many farts will his tin of beans produce?"

My answer is 12.7*






*.3 = solids

Re: How many beans are in this tin?
 

me counts da # ov Bs onda labbel - it tell me dat is but 31 beenies in da tinny.

Re: How many beans are in this tin?
 

Unfortunately just a small update on this important matter (as I had to spend the last couple of hours on the phone with "customer service" making a trivial modification to an internet purchase I made this evening "We can't do anything about it as part of the order has already shipped"..."I just want to swap one of the items in the order which hasn't yet been shipped for something which is the same price and more correctly matches with the rest of the order". "Sorry sir, we seem to be talking in circles...When you receive it, phone the manufacturer" :confused:). I finally got to talk to a manager, I think he fixed the issue by cancelling the original order and doing up another one. No doubt I'll receive both orders and be charged double.

Back on topic. I received an email today, a wordy hypothesis on the subject, however I'm currently unsure how to summarise it other than to say its something about "protein content" and "the proposed number of whole beans is 467". I'll post it up in more detail later.

Dear daughter is primed and ready to count the beans tomorrow :wub:

Re: How many beans are in this tin?
 

I'm really interested to see if someone can apply pure math to come up with a closer answer than 4009 though. If anything, to make us math-heads look a little more respectable on here... :)


I suppose it's up to Novo, as he posed the question. I think if there are, for example, two half-beans, then they should be totalled up as one bean and added to the count. However, I'd also suggest that the word 'bean' should probably be interpreted as the "solid state of bean", rather than any other state. So any bean mush or bits that no longer resemble that usually recognisable "bean shape" should be ignored?

You know, while deciphering this, I realised that as soon as we open the tin and empty the beans out to count them.... there will be zero beans in the tin :confused:

Re: How many beans are in this tin?
 

I think you're creating a false duality by only counting the beans. They have other qualities, like taste, texture and of course social implications of consumption. You maths people only see the world one way, that Descartes fellow has a lot to answer for. :frown:

Re: How many beans are in this tin?
 

Around here beans are refried, the resultant paste must contain more beans per cubic inch than the whole, or nearly whole, offerings from Heinz. I'd be interested to compare but need a method for reconstituting the refried beans, would sculpting be adequate?

Re: How many beans are in this tin?
 

Are'nt there any Accountants (Bean Counters) reading this forum ?

Re: How many beans are in this tin?
 

Actually counting the beans, is the work of a 7 year old, who I'm pleased to see hasn't yet accomplished the task.

This is because I've just figured out the error in my result. The problem is that the prolate spheroid beans can't pack as efficiently as spheres. Doh.

Back in 1921 there was a paper on this topic concerned with X-ray powder crystallography, which I remember reading at the time. :) Here's the link....

http://prola.aps.org/abstract/PR/v17/i5/p571_1

Basically, the close packed spheroids align so as to occupy a volume with average spacings equal to approximately twice their minor diameter times 1.5 their major diameter.

This means that the effective volume occupied by each bean, compared to their physical volume needs to be increased by 2x2x1.5 = 6. So my earlier, extremely naive, estimate needs to be appropriately reduced from 4009 to 668.

And that's gotta be right.

You can open that tin now and confirm my triumph of intellect over BE junk food.


Edit: Oh, and in passing, may I rubbish the analogies to Schroedinger's Cat?

This issue there is whether the cat is alive or dead, not whether the cat is still in there.

Re: How many beans are in this tin?
 

I have an old university accomplice who is the Financial Controller for Heinz near Manchester. A Bean Counter in every sense......

Therefore I am declaring myself out of the competition due to having the availability of inside knowledge.

Re: How many beans are in this tin?
 

My bad, I should have posted the other day that the lunchtime phrase "Daddy, I'm hungry" caused an event that meant the bean tin was opened and the contents were soon after consumed.

All is not lost though, prior to eating, I spread the beans out on three plates and photographed them. I also took a photo of the inside of the can as there was a long-ways half bean stuck in the bottom of it.

I'll post them up so we can all count them to ensure an accurate total.

Having eaten a plate of them, lucky me (that I had some rantidine in the cupboard ready for the aftermath of such an adventure), I suspect your new estimate of 668 is probably very close.

I'll upload the pics from the camera after I gave the beef curry a big stir.

Oh, I also believe "prolate spheroid" is not really a very accurate mathematical description of the objects that came out of the tin. More like the offspring of Mrs. Prolate Spheroid and Mr. Amorphous Blob-Randomly-Divided. If there's specific mathematic terminology to describe such an object I, as well as at least one other forum member, will be well-impressed.

Re: How many beans are in this tin?
 

668, right?

Re: How many beans are in this tin?
 

I will not comment at this time on the ill-advisability of involving 7 year olds in serious scientific investigations.


Oh joy!

Goes without saying, innit?

Cheap beans. Get a proper UK tin.

Re: How many beans are in this tin?
 

If I'm honest with you all I think there has been an over site in how you are all approaching the problem.

The configuration of the sophisticated manufacturing equipment at Heinz will no doubt work with weight of beans rather than number and therefore there is likely to be a deviation in results as it is unlikely that every baked bean is the same size.

Therefore when people are calculating we need to really be thinking mode rather than mean and also attention needs to be paid to deviation.

In conclusion what I am trying to say is that the only way this contest can be bought to a fair conclusion is if Greenhills seven year old counts the beans in multiple tins????

Some one is definitely going to be demanding more pocket money!

Re: How many beans are in this tin?
 

God! Now you want error bars?????