Boxes and Coins: Newsletter Challenge (06/12/07)

Pedants? I see no pedants. Now where's that mirror?

Fyz

Ha-ha. All will become clear.

That's a great solution. It could even be new...

Fyz

Excellent solution. The type of scale is not specified so why not! This fits the question better than all the other answers I've seen.

Hopefully, the pivot is above the C of G even after you have placed the boxes - or the doubters are correct and everything falls off.

On the other had, if this starts its life on a flat surface, you don't need to raise the pivot that far...

Fyz

Start loading the scale in the following order, one box on the left side and one box on the right side, check the scale for balance, if the right side point heavier than the box on the left side is the bad box, orvisa versa, if the scale is in balance continue with the next set of boxes, one left and one right side, check scale again for balance or inbalance the first time an inbalance occur and scale tips heavier to one side then the opposite side will be the bad counterfeit box, if need be continue to all ten boxes may be needed to be loaded on scale to find the bad counterfeit box.

Frank

You cannot have left side and right side scale. As this will need many 'weighings'. The radial ring in plane is the only way to have one weighing/reading.

KennyT

A single differential weighing (e.g. post#20) using a standard laboratory balance works as well. I think we'll find that sort of thing is what the questioner intended - that just makes your solution even more pleasing.

Fyz

There appear to be several problems with this question. The first being the definition of one weighing. I would consider that to be one placement on the balance and one reading of the display. Surely removing boxes one by one is multiple weighings.

My second problem is that it doesn't specify what type of "scale". The old fashioned arrangement where you can employ differential weighing or the more likely single balance?

And finally, just to be picky; it simply states that the box of counterfeit coins are 5g lighter. No where does it say that this shortfall is divided evenly among the coins within the box. Possibly, due to the dodgy process used to make them, some of the counterfeit coins are heavier and some lighter with the net result being a 5g shortfall?

I await the solution with interest as I can't see how it can be done within the confines of the question.

I believe Hendrik was on the right track in Post #20.

On a levelling balance you do not have a weighing until you have a balance between the sides.

Place boxes 1 - 5 on one side and boxes 6 - 10 on the other. The lighter side has the box of counterfeits. Add a 5 gram weight to the lighter side. You have your weighing, but you still have not found the box of counterfeits. You now have no need to concern yourself with measuring weight, just finding the box of bad coins.

Remove a box from both sides of the scale. If you have removed two boxes of good coins, they weigh the same and you should still have a balance. Repeat until you no longer have a balance. The side with the 5 gram weight is now the heavier side because you removed less weight from that side. The the box you just removed from that side is the box of bad coins. Of course, if you remove the four good boxes from the side with the bad box, the bad box remains with the 5 gram weight, you still have balance, but you have identified the box of counterfeit coins.

Why add weight? Place all ten boxes on the balance,five aside. Remove one from each side at the same time and check for balance. The weight will be unequal until the fake box is removed. It covers all the bases the boxes have only been weighed once and no mucking round with numbers, coins or weights.

Post number 20 genuinely achieves a single weighing in the usual sense of the term. If instead of adding weights, it used a modern digital differential balance, the difference between it and your multiple balancing acts would be even more marked.

It seems #20 is the right solution, but contains many assumptions.

Such a challenges always miss important info, like:

1. Balancing scale or not?

2. If balancing, we may observe the fact of mass difference or weights (or accurate readout) are available?

3. "Box of bad coins weighs 5g less" - maybe due to box weight, not coins?

4. Does the 5g distributes evenly among 100 fake coins?

RF

It is a "very accyurate scale" - just vertically stack all the boxes and use the difference in gravitational pull to figure out which one is not pulling the proper force.

Take 1 coin from box 1, 2 coins from box 2, 3 from box 3 and so on. That's a total of 55 coins. Put them all on the weighing scales and take the reading. We will have to assume that we know the weight of a good coin which for example is 50 grams. If all the coins weighed the same then the total weight should be 2750 grams. If the actual weight is 2745 then this means that box 1 contains the counterfeit coins, i.e. the total weight is light by 5 grams or 1 counterfeit coins weight. If the total weight is 2740 then it is box 2 and so on.

Alan.

Since the weight of counterfiet box is 5 gms less each coin in that box weighs 50mg less. to know the exact box with counterfiet coins take 10 coins from box no.1, 20 coins from box no. 2 .... and so on. Put them on the weighing scale. If the box no 5 is faulty the weight shown will be less by 250 mgs. ie. weight shown less divided by 50 will give you the faulty box no.

If the box no 5 is faulty the weight shown will be less by 250 mgs

250mg less than what?

Davo

With each box numbered, 1 to 10, take the number of coins out of each box that is equal to the number on the box. So box numbered 5 you would take 5 coins out. Having removed the coins from the boxes weigh all the boxes at the same time. The box with the counterfeit coins is then easily determined from the total weight. Each counterfeit coin weighs .05 grams less than the good ones.

10, 9, 8, 7, 6, 5, 4, 3. 2, and maybe ending at only 1, weighed together, removing one at a time. The odd difference is the boogy.

Put all ten boxes on the high accuracy scale and note the total weight. Remove one box at atime and note the drop in weight. The box that has the lower drop in weight compared to the other nine boxes is the box that contains the counterfeit.

Multiple weighings again

I think the problem is only solvable if you know the mass of a good coin. As they are coins, this information can be found (try Google!) without a weighing. Put the 55 coins on the scale and solve for the box number: BoxNum=(55*CoinWeight-TotWeight)/(CoinWweight-0.05)

Ricky Lee

Australia

With the assumption that the real coins weigh some whole number amount and deducing that a bad coin weighs 0.05 g less than a good coin we can try this approach. This way we can deduce the counterfits with only one weighing.

Remove a progression of coins from each box in turn 1,2,3, .... 10

Weigh the set of removed coins on the very accurate scale.

The fractional remainder on the scale reading divided by 0.05 is the box with the counterfit coins in it.

(NNNN.dd - NNNN) / 0.05 = CC

...........................

OK, I may be way off on this but thats what you get as a "first thing in the morning without me cupa tea" answer

I think you are all missing the point completely. There is only one way to weigh only ONCE in true terms. That is is with all the boxes on the balance at the same time refer to my first explanation. The balance is a flat round plate with the center removed leaving a flat ring. The flat area between the inside diameter and the outside diameter being sufficient to take the boxes. As we don't need to know the size of the boxes. Then in plan view you place the 10 boxes at equi distant placing throughout the 360deg's. The flat disc is suspended from one point in the center and left to settle and as I have said before you will see the lightest side in "SIDE VIEW" raise slightly higher. The box at the highest point is the lightest. No need for spreadsheets and differential calculations. This is ENGINEERING at it's most basic level. Why all the fuss?

KennyT

That's too easy. This has to be a logic question. "Allowed one weighing" on a standard (not tilting) scale. There's bound to be a way to do it, hmmmm...

Hi Steve

It does sound too easy but it works 'I have done it' Why look for the hard way out to simple problems. Work smart not hard.

KennyT

Hi Steve

I could not see that it has to be a "standard" scale. It simply says 1 weighing.

KennyT

"Using a very accurate scale" was the exact phrase in the question. A "flat round plate with the center removed" was your solution. That doesn't sound like a scale to me.

Good solution, provided you can place the coins or boxes of coins accurately enough. I guess you could verify your accuracy by placing only one type of coin around the perimeter.

"There is only one way..." Brave statement.

Davo

Although you came up with the basis of an elegant solution to the problem of identifying the odd box, to my mind you are spoiling things by insisting that yours is the only solution to the problem as posed.

First, the question does not specify either the location of the centres of gravity within the boxes, nor that you can identify the location with respect to the outside of the boxes. For all you know they could be perfect cubes externally, but with a well-offset centre of gravity. You can of course solve this by making the ring large enough, but then you have to build it specially, rather than using already available equipment.

The question specifies that you are to use a very accurate scale, and that you are restricted to one weighing. Typically, accurate scales are laboratory balances. This is a technical site, and the technical meaning of weighing is a process that determines a mass or weight. "A single weighing" would include multiple additions and subtractions of calibrated weights as part of the process of establishing a weight (or mass) - after all that is the time-honoured method of weighing used by chemists and physicists. Admittedly, we have to make assumptions - that the mass difference is in the coins and that the counterfeits are identical - but I would put this down to the usual level of terseness in the question.

That would make #20 and its related arrangements conform to the spirit of question. Most of the others include multiple balancings of different combinations of coins rather than a single weighing - so we could count these as zero weighings, conforming to the letter if not the spirit of the question.

Finally, elegant as your method is, it does not inherently conform to the instruction that specifies "using a very accurate scale". Your method uses a sensitive balance - and sensitivity is not the same thing as accuracy. So you would have to build this to be part of an accurate set of scales to satisfy the constraints (which would be rather artificial, I think).

So, congratulations again on an innovative and elegant solution to the problem of identifying the forgery in a single measurement. But to actually make it work would be a lot more trouble than using the precise scales that are specified to be provided.

Fyz

I think it best I refrain from any further comment as it is not my intention to spoil anything. Only to state what I have actually done in the field. Without the benefit of a Physicist or any laboratory equipment in sight. I have read the question as a legal document and it does not allow for the all the interpretation that I have seen so far.

I'll await the outcome with enormous interest.

KennyT

I keep forgeting to log in so this may be in duplicate.

I think it best I refrain from any further comment as it is not my intention to spoil anything. Only to state what I have actually done in the field. Without the benefit of a Physicist or any laboratory equipment in sight. I have read the question as a legal document and it does not allow for the all the interpretation that I have seen so far.

I'll await the outcome with enormous interest.

KennyT

Here Here

A sound summary of the situation.

Why would you see the "lightest side in "SIDE VIEW" raise slightly higher" ?

What stops the lightest side from raising lots higher. What stops gravity from pulling the heavier side all the way down as far as the mechanism allows it to travel ?

No matter how small the imbalance in mass, the imbalance never ceases to exist so why does gravity only pull it a 'slight' distance ?

Do light aircraft only fall partway to the ground and heavy ones go all the way ?

You haven't made an engineering error here have you ?

I will come back in on just this one. balance scales work on proportional difference. when you measure something on a balance scale it will only tilt proprtionaly to the other side. Sadly an aircraft falling to earth only has gravity effecting it. If they only flew round poles with a counterbalance they would not have to worry so much.

My scale will have genuine and heavier boxes either side of it (36deg each side) so the difference will show slowly and have a terminal point. Not crashing into the earth as you worry it will do. Engineers, Physicists, Mathematicians etc do make mistakes and it is good to get sound counter discussion to ones ideas. However having seen this work to my design I have a fair level of confidence. It does as Physicist pointed out assmume a common center of gravity within each box.

KennyT

So if I put a big kid and a little kid on opposite sides of a seesaw they'd hover in mid air at an angle determined by their differences in weight ?

Likewise if I put a big monkey and a little monkey on opposite ends of a rope which was around a pulley attached to the roof, the monkeys would be suspended in air a distance apart as determined by their differences in weight ?

Now if we had a spring somehow incorporated in the balance mechanism then I could see that as it compresses / extends, it's ability to oppress forces changes and a balance could be reached. But when we rely merely on gravity then I don't see how a balance is achieved. The imbalance in mass remains unchanged, the lever lengths are unchanged, gravity is constant so I can't agree with your point.

If I only tilt the plane a little way, will the sphere only roll a little way ? If I wanted the sphere to roll all the way off the plane do I need to tilt the plane a large amount ?

It all depends on the location of the centre of gravity relative to the pivot. KennyT's design as I interpreted it would have had the ring suspended, so the centre of gravity is below the pivot, and the ring will come to rest in a stable position. A see-saw is deliberately not designed for stability - if the ground were not in the way, most of them would have a stable position - but upside down.

Fyz

Negative Phys.

The centre of gravity arguement only works for a singular weight, not a collection of independent / separate weights.

Would you argue that in the ferris wheel example, the slightly lighter box/seat would not migrate all the way to the top of the wheel, but rather somewhere slightly above the 90 deg or 3 o clock position. It's the same situation.

The unloaded Ferris wheel is equivalent to neutral in stability terms. The lightest point goes to the top.

KennyT's weights are not independently suspended. They are on a rigid surface. The method of suspension determines the sensitivity (or level of stability)

To see what happens in an approximately realistic case: get an unwanted CD or DVD (=disc), and some string. Cut and tie the string so that you have three strings coming from a central point, and place the knot under the middle of the disc. Bring the strings up about a foot above the disc and join them so that the join is perpendicularly central to the disc. Place weights in various positions around the circumference, and lift from the join in the string.
N.B. I have made it a foot because the disc is rather smooth; this is to avoid the weights sliding off the side under near-worst-case loading. If you make the join closer to the disc, the tilt for a given arrangement of the weights will increase. So you can adjust the sensitivity to match your requirements (by the changing the height of the suspension point above the disc).

Positive!

Fyz

Does my rather excellent drawing help ?

The 3D version is beyond me. Still , I wonder what would happen in my doodle with 10 coins one side and 9 the other. I should have drawn the pivot closer to the heavier side , but I'm to lazy to do it proper. hmm

If you try bouncing your arrangement like that squirrel, you will never again know which coin came from which box...

Fyz

I kneel in admiration !

This is the closest to a 3D prototype image that I can do from home. This is the very basic design to support my first statement. The pin indicator extending from the bottom is a simple indicator of how much the plane inclination is and can be used when calibrated to indicate weight differences.

As I have some copyright interest in the full production model I can't go beyond this explanation. I hope it shows the very sensitive nature of the instrument and helps allay some of the doubters. The Oz hanging cork hat principle could be included if C/G of the items was a problem.

Kenny T

Nice. I see that you too keep your defunct CDs for general applications.

Does the 'proper' version have an adjustment for pivot height in case the CofG of the boxes is too high - or would you just forget the needle and rely on not lifting the plate too far*?

Fyz

*For general readers - the lightest box would be opposite the contact point with the (presumed flat) table.

Nice.

And to Guest 180 - surely you had to do those calculations in physics/Applied maths where you calculated the critical angle of an inclined plane at which the sphere would begin to roll - and the angle at which it would slide?

It is possible to have the seesaw at a non-horizontal equilibrium where neither end is on the ground. My sister and I (at my instigation) used to demonstrate this: she (younger and lighter) sat in the seat, whilst I moved towards the pivot point until we were about balanced. Either side of this point, I could get the seesaw to balance with both of us in mid-air and the "plank" at an angle.

If the see-saw didn't balance when you weren't sitting on it, either you were lowering the centre of gravity, or (more likely?) you were (unconsciously?) providing active stabilisation by moving your Cs of G in and out to maintain an otherwise unstable equilibrium.

Fyz

No, Spheres and Planes is engineering at it's most basic level.

Incremental gravity as described by yourself is a facet of your imagination.

So far , I have not noticed the effect while rolling down the stairs after a heavy night out.

The actual extremely accurate wieght of the 55 coins selected as in Post#1 if all coins were genuine would be exactly divisible by 55. There are 10 possible errors introduced by the fake coins all are negative weights of .05, .10, .15, .20, .25, .30, .35, .40, .45 and .50 grams. So dividing the total weight of the 55 coins will not be exactly divisible by 55 but if divided by 54 will leave a remainder of 0.95 grams (Box 1) to 0.5 grams (Box 10)

Dear Extremist,

Please go back and read posts 17, 18, 19, 21, 23, 32, 33, 34, 35, 38, 44, 49, 80, 91, 97, 124, 101, 110 and especially 121 with follow-up in 123 and 126 for a complete discussion on this method.

Post 121 is the critical discussion of why this method does not always work .... although it ususally does work.

Dwight

I think that for the intent of this question as described we must assume that the weight of each genuine coin is exactly identical to all other genuine coins regardless if it is nnn.xxxxxxxxxxx--- grams. The weight of each fake coin is also identical to to all other fake coins which is .05 grams less than a genuine coin.

Regards

The Genuine coins are made of 24carat gold the fakes are iron pyrite. The Weightmaster takes 10%

Don

Are the gold coins are hollow, or do they only weigh about 68-mg?
Most unusual...

Fyz

They weigh one ounce exactly

I realise that converting the actual measured weight of the sample coins to $value of gold would require a huge active damper on the scale to keep it from fluctuating long enough to get an accurate reading.

So how do you explain the difference in mass between a gold coin and an iron pyrites coin of the same appearance being only 50-mg?

It was weighed on a very bad day for the gold market so the weight of gold vs pyrite became much closer by mass!

Or perhaps a good day - the gold lifting itself by virtue of its own exuberance, and placing minimal weight on the scale?

I thought I was wrong once but it was a mistake

It was twice ? No. Have confidence in yourself.

OK!

My barber said "I cut your hair TWICE! and Its still too short!!"

Everybody thinks I'm unbalanced. theyjustdont-understandme

I went into the fish and chip shop I said.

'Cod and chips twice please'

The guy said.

'I heard you the first time!'

Quite - but please return Mr. Plancks apostrophe before 'them other pedants' set the thought police on

Fyz

Planck can't. It's apostrophe's to give. Planck's possesionless.

Now that raises incoherence to a new level.

Fyz

I have to admit that KennyT's solution might be the best for its simplicity and elegance. But how often has anyone seen a scale like that? The closest thing I have seen is a bubble balancing device for balancing tires. For someone working in a bank, they are most likely to use a balancing scale or a scale with a dial or digital readout.

Now let me add another twist from my experience: one weighing does not necessarily mean one reading. Years ago, I sold a load of scrap metal. I drove my pickup with the scrap in the bed onto the scale and the operator took a reading. Then after unloading the scrap, I drove my truck back onto the scale, and the operator took another reading. After subtracting the second reading from the first, he had the weight of the scrap he paid me for.

You need a Tare 3Doug.

THAT was the word I was trying to think of!

It would still count as 2 weighings tho...

________________________________

Vas disch un buttrum massegr marn?

So again we return to terms of reference. 'weighing'

If we weigh only 10 coins the accuracy of measurement has to be down around 0.005gms. If we weigh 10 boxes it is 5gms. both possible with any scientific scale.

Using the swinging dish would meet the criteria of a single weighing, as in one stacking. But adding one element/unit at a time amounts to the same.

Tare is part of the weighing process, not a second weighing...we calibrate everything else...why not a scale?

The next term is how do we determine a difference in weight without a second weighing? (difference of good and bad coins)

Ergo efforts must be combined/in conjunction to achieve this outcome.

Hi 3Doug

I think the weighbridge you describe is legaly a 2 weighing system. I have read the question again and I can't find anything about the "bank" scales you mention.

Look up the definition of scales in the Oxford dictionary, and you will see where I'm coming from.

I have lived and directed major engineering projects all around the world, and the people in some of the emerging nations have only simplicity on their side. So I have learnt an awful lot of unorthodox methods over the years on top of my formal education. Good discussion though, so far.

KennyT

Hi, KennyT.

I have to admit I sometimes overthink situations, and sometimes I just like to stir the pot, so to speak. You should see some of my posts on the Stormtrack.org forum!

You posted your solution while I was still composing my orginal post. That's why I said, once I read it, that yours may be the best, at least theoretically.

Concerning the types of scales, I was thinking of the types that are wdely available because radial balance scales are not commercailly made AFIK. Most scales use weights of known mass and balancing mechanisms, or springs. For someone to use a radial balance, they most likely would have to build one themselves, or have it custom made. Plus, the plate itself would have to balanced.

From the wording of the problem, we can infer that someone else has already examined and weighed the coins. But now that person either cannot remember which box has the counterfeits, or they quit, got fired, got sick, died, or maybe gone on vacation and can not be reached. It is now our job to identify the counterfeits, and we have to use the equipment at hand, and quickly too.

Now for another twist, or stir of the pot, if you will.
The problem did not say we had to weigh the coins, only that we are restricted to one weighing on the scale. Let's say that a single weighing involves the placing of an object or objects on a scale and taking one reading. We may add or subtract items as long as we take only one reading. It may be that the only weighing we need is the one already done.
With the radial plate, no reading is necessary, because you are not reading the weight, you are only looking at how the coins balance. Same with the method I described in my second post, #95. I believe Hendrik gave a variation that simplified my method.

This is a problem that, as given, might have more than one solution in the real world, given the different types of scales available. I will now wait for the "official" answer, but I will still monitor this thread to see just how complicated this dsicussion can get.

Boy, engineers sure can complicate things. Assume that the boxes of good coins weigh 100 grams each. Put all of the boxes on a good triple beam scale. They should weigh 995 grams. Take the boxes off 1 at a time. The good coins will subtract 100 grams each. The bad box of coins will only subtract 95 Grams. No brainer!!

Poundkatt

And for those that like to nit pick, once you put the boxes on the scales all together, that is one weighing, you can take them off any way you prefer, and I prefer to take them off one at a time. I am not obligated to close my eyes & not look at the scales as I take the boxes off.

Let's hear it for the Katt, Poundkatt

I'm an "Engineer" and simple is normaly best. Your proposal is still multiple weighings though.

KennyT

OOPS!! I goofed. For triple beam scales, read digital postal scales. Now 1 Weighing.

Poundkatt

Hi Poundkatt, I think your obvious 'solution' is stretching the limits of interpretation of the question to the point of being infantile. If this was the real answer then I can only wonder how the question was mistakenly called a 'challenge'.

Sorry to be rude, but you asked to "Hear it for the katt" (?) Davo

I cheated and googled the answer.

It would appear that there was an omission of information in the question given.

We're supposed to know the weight of a good coin.

Can still be done without the knowledge of the weight of the coins. It could be cheese we're comparing. Forget the coin weight and "Engineer" the resolution.

KennyT

I did engineer the solution. Information is where you find it and the puzzle didn't add up. Stop trying to invent a square wheel.

It's not the "Engineering" That anybody I know would call"Engineering" I call it cheating in a test of application and innovation.

KennyT

It's not cheating, it's life. I only googled the answer after the arguement had been thrashed to death, and I'd read the answer that I agreed with in Post # 84. It was because I agreed with that response [ie we need more information] that for me the puzzle was over.

And while you're busy engineering stuff, why don't you sit one box per seat on a perfectly balanced 10 seat ferris wheel, let the ferris wheel 'free wheel' and wait to see which seat rotates to the top of the ferris wheel ?

Despite the fact that this would constitute a weigh / balance mechanism, it's obvious that the spirit of the question intends us to use a simple [albiet appropriately accurate] weigh scale. Not a beam balance nor a fanciful invention.

it's obvious

I don't agree. On top of that , what does the question mean by "very accurate" ? Good enough for the job I'd say. A ferris wheel is a good solution , just the same as a horizontal disc . If you take things to literally and serious , you'd be stuck if stranded on a desrt island trying to figure which box held fake treasure. Archimedes should have drowned himself - he wasted time on an elegant and simple solution.

What I propose is not a fanciful invention. A scale is a balance, normaly between 2 items. a radial balance is merely an extention of that principle. I see it made you think. As the principle can be inverted but due to central gravitational loads on the bearing hub a ferris wheel would simply take a little longer to reach it's offset equilibrium. Keep thinking. One day you may want to be an Engineer as well.

KennyT

I think the radial balance is an excellent solution. If they forgot to tell us the weight of a good coin, well they also forgot to tell us what type of scale. No information cuts both ways!

If I had 5 bob, I could weigh the coins and use the knowledge to solve the problem. If I had a quid I could build a radial scale.

Just Kiddin', your comments are a fair cop.

How would you feel if you were the client, you hired an engineer to solve the problem, you locked him in a lab with the coins, a set of digital scales, a pen and paper. You come back later to see how he's progressed and he's drawn you a radial scale [or maybe a ferris wheel] and asked for more money to build it [or maybe just asked for circus tickets].

The problem faced by many engineers is that they can always see an alternative method to what the client proposed and have dificulty accepting the clients wishes.

The beauty of many engineers is that if the problem truely cannot be solved using the clients concepts is that they'll come up with an alternative solution.

The true skill of course is to identify each scenario and work as required. This is the skill that will gain you a sound reputation and get you rehired for the next task.

I agree that your horizontal radial scale will work, as will my vertical one [ferris wheel], I'll apologise if I seemed abrupt, and if we put ourselves into the clients shoes what would our end solution be ?

PS The client will -as always- be crying poor because one of his boxes of money is fake .... and somehow that's the engineers fault ;-)

The point here is that the clients brief is, well, brief! We are given some facts and a constraint(one weighing) and asked for a solution. The radial scale is a solution that fits the facts and accepts the constraints. Any thoughts of the customers reaction when being presented with a bill and a radial balance (or a well balanced ferris wheel for that matter) are as much conjecture as saying that you could google the weight of a good coin.

Possibly the customer has thousands of these sets of boxes and wants a quick way of finding the light box. The radial balance could be purpose designed to have a digital output that indicated instantly the dud box. With locating lugs on the plate it could be operated on a production basis. The biggest problem I can see is how to ensure the C of G is the same in each box. Perhaps the boxes could be suspended below the balance plate?

But you'll agree that it's alot easier / quicker / cheaper to ask the client for the weight of a good coin ?

If you consider that to be outside of the contraints of the question then you may also note an earlier post [it might have been Davo .. can't remember] who raised some points that the radial balance doesn't fit within the constraints of the question.

Try physicist, post # 122

Can't say I remember a post along those lines, not one I agreed with anyway! Can you remember where?

Why doesn't a radial balance fit the bill? I thought the only constraint was one weighing, there's no information given on the type of "scale" except that it's very accurate. Fine, build a very accurate radial balance! Such things exist already.

Also, to be fair to the radial scale, if the boxes were suspended via a single contact point, they'd find their own centre of gravity directly under that point [which I think you alluded to].

I think the arguement against the radial scale fitting the constraints of the question was that we are provided with an extremely accurate scale, whereas the radial scale has no accuracy, merely it has [an appropriate] sensitivity.

Not at all. Consider a tyre balancing machine; gives a readout as to where and how much weight is required. A purpose built coin weighing balance could easily indicate which segment is high/low and by how much. A good one would be accurate, a bad one would not. We're told to use a good one!

Doesn't a tyre balancing machine spin the wheel and measure the imbalance in centrifugal force to indicate the where and how much weight to be added. If this is what you mean then fair enough it's concievable to build an equivalent device to solve the problem, and it would be considered to have 'accuracy'.

There was an old fashioned method to balance tyres which didn't involve spinning the wheel, but rather had them laying flat on a pivot and a spirit level was used to pick the light point, but it couldn't tell you how light that point was [balancing weights were added incrementally] hence it had no accuracy, just sensitivity.

Ahaa .... theorectically though, the spinning tyre balancing machine would constitute multiple weighings because it's essentially one weighing everytime a point [or box] passed the load cell.

It's really just a machine that takes multiple readings for one loading of the machine, henceforth ... it cannot be used.

Wow, things have moved on since I was last here, 230+ and it's no where near Tuesday!

Anyway my comment re tyre balancing machines is being taken too literally. I was merely pointing out that the concept of location and mass is not unknown. A tyre balancing machine is a dynamic balancer which is not needed here.

I actually like KT's CD balance but the pedants are saying that it lacks accuracy. I see no reason why such a balance couldn't be built to give acuracy as well. My thoughts run towards the plate being supported on three load cells, arranged in a triangle. The boxes are suspended from ten hooks arranged in a circle around the load cells. Take the output from the cells and crunch the numbers. I'm fairly sure that this would give the information required. Accuracy limited by quality of build.

meaning of course that 'each' box were suspended by it's 'own' single point of contact.

Alrighty ... this is my last thought on the subject.

KennyT's machine could be considered to have accuracy if we were to say that it could accurately determine the location of the different weight box, acknowledging that it couldn't determine the [amount of the] difference in weight.

By this definition, the radial scale has accuracy.

See ... I'm fair !