Greenhill

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

Greenhill

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.

fledermaus

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.

Greenhill

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)..

Novocastrian

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.

fledermaus

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

magnumpi

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

For that reason i go for 317 beans.

Greenhill

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)..

Novocastrian

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.

Novocastrian

Are you channelling immichaelcaine?

fledermaus

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

Novocastrian

Frozen beans? No thank you.

Greenhill

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"??

PeterF

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

We said 248, wrong of course.

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

Novocastrian

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.