[Guest]

You are in an office on the 10th floor of a building. It is 3 am on quiet summer night. There are ten bags filled with lots of gold coins. One of the bags is filled with faked gold coins. They are identical to the real ones except they weigh slightly more. You may not leave the office until you find three ways (at least) to determine which bag had fake gold coins.

assume normal office supplies, MacGyver.

* oh the scale you had planned use is broken.

** as a rookie not sure if this truely constitutes a puzzle but I hope it is of some interest.

[Guest]

You are in an office on the 10th floor of a building. It is 3 am on quiet summer night. There are ten bags filled with lots of gold coins. One of the bags is filled with faked gold coins. They are identical to the real ones except they weigh slightly more. You may not leave the office until you find three ways (at least) to determine which bag had fake gold coins.

assume normal office supplies, MacGyver.

* oh the scale you had planned use is broken.

** as a rookie not sure if this truely constitutes a puzzle but I hope it is of some interest.

Well, if the office has bags of coins in it, then chances are, there are more bags available. I would take a number of coins (lets say 25) out of each bag, putting them in 3 seperate bags. Given that the fake ones weight more, then 2 of the bags would feel the same weight, and one heavier. An individual coin would not be enough of a difference to feel, but a larger amount of coins would. Thats one way to find out.

Another would be to take one coin from each bag and spin them. I admit I don;t know the math and all, but I do know that the speed/length of time of a coin spinning is effected by the weight of the coin. So, two coins would spin the same, while the other would not.

Take a coin from each bag and drop it down the elevator shaft. Time the fall of each coin. The one that hits the ground fastest is heavier, and thus fake. Given that it is a summer night (morning actually, since it's 3AM) it is likely to be warm, so the sound will travel better, plus it's 3AM, no on should be there, so less noise to distract.

Thats all I can think of. And I can't find anything on the math for my second answer..

[Prime]

...

Take a coin from each bag and drop it down the elevator shaft. Time the fall of each coin. The one that hits the ground fastest is heavier, and thus fake. Given that it is a summer night (morning actually, since it's 3AM) it is likely to be warm, so the sound will travel better, plus it's 3AM, no on should be there, so less noise to distract.

...

Two objects of the same shape will take exact same amount of time to fall down the elevator shaft regardless of their weight.

You could suspend coins from each bag in turn on a same rubber band and measure how far it stretched.

[Guest]

As much as I know, any ordinary metal weighs always less than gold. Only platinum has more density than gold, and I think it's more expensive than gold, so it can't be used for fake gold coins. But if the coins have cavity in them, ordinary metals can weigh more, if their cavity is less than gold coins. Anyhow, here are my solutions:

tilt the table, roll one by one coins from each bag. As the gravity force applies more to the heavier one while friction force is identical, rolling time to end of the table and rolling distance after the end of the table differs.

Leave same count of coins in two bags. Tie these to end of a 2 meters cable. Place a pen beneath the cable and hang the bags. The heavier bag pulls the other one and goes down. If you loosen the lit of pen, it will ignore the effect of friction. (Excuse me for bad eng.)

I have a ventilator in my office. If you have too, leave the coins one by one in front of and above the ventilator. Heavier ones will drop closer, while lighter ones will be blowed by ventilator and travel more in the air.

[Prime]

As much as I know, any ordinary metal weighs always less than gold. Only platinum has more density than gold, and I think it's more expensive than gold, so it can't be used for fake gold coins. But if the coins have cavity in them, ordinary metals can weigh more, if their cavity is less than gold coins. Anyhow, here are my solutions:

tilt the table, roll one by one coins from each bag. As the gravity force applies more to the heavier one while friction force is identical, rolling time to end of the table and rolling distance after the end of the table differs.

Leave same count of coins in two bags. Tie these to end of a 2 meters cable. Place a pen beneath the cable and hang the bags. The heavier bag pulls the other one and goes down. If you loosen the lit of pen, it will ignore the effect of friction. (Excuse me for bad eng.)

I have a ventilator in my office. If you have too, leave the coins one by one in front of and above the ventilator. Heavier ones will drop closer, while lighter ones will be blowed by ventilator and travel more in the air.

Lead is heavier than gold. And it is common enough.

Also, your gravity test would not work. Especially so with the assumption that friction is the same. In that case coins of different weights will roll down at the same rate, same as free fall.

Fill the sink with water. Take a plastic cup, put in a certain number of coins. Let cup swim in the sink and measure what part of the cup submerged.

[Guest]

Lead is heavier than gold. And it is common enough.

Also, your gravity test would not work. Especially so with the assumption that friction is the same. In that case coins of different weights will roll down at the same rate, same as free fall.

Fill the sink with water. Take a plastic cup, put in a certain number of coins. Let cup swim in the sink and measure what part of the cup submerged.

Density of lead=11.35 g/cc while gold=19.30 g/cc

Different weights will NOT fall at the same time. I read the article and it says air resistance is neglected.

Rolling must work, I suppose. A rolling coin on a tilted table, gains an amount of kinetic energy. This energy is consumed when it finishes the table and begins to cope with the friction on the ground. A heavier coin will gain more kinetic energy and as the friction is same, it will travel more distance??????

And; my gravity test is a kind of scale (suspended coins), why wouldn't it work?

Edited November 26, 2008 by nobody

[Guest]

Density of lead=11.35 g/cc while gold=19.30 g/cc

Different weights will NOT fall at the same time. I read the article and it says air resistance is neglected.

Rolling must work, I suppose. A rolling coin on a tilted table, gains an amount of kinetic energy. This energy is consumed when it finishes the table and begins to cope with the friction on the ground. A heavier coin will gain more kinetic energy and as the friction is same, it will travel more distance??????

And; my gravity test is a kind of scale (suspended coins), why wouldn't it work?

But is the friction the same? The friction surely varies with the amount of force appleied between the two surfaces, and the heavier coin will be pushing down harder on the table creating more friction... just like pushing the brake harder slows you down quicker cos more friction is created.

[Guest]

Bad luck about proving it... Just grab three bags and make a run for it... chances are small that you would grab the bag with the fake coins... and who would care with 2 more bags of gold on board!!!!!

Just my way of saying... I have no &*%$%%& idea...! Whoops think I swore then... sorry

[Prime]

Density of lead=11.35 g/cc while gold=19.30 g/cc

Different weights will NOT fall at the same time. I read the article and it says air resistance is neglected.

Rolling must work, I suppose. A rolling coin on a tilted table, gains an amount of kinetic energy. This energy is consumed when it finishes the table and begins to cope with the friction on the ground. A heavier coin will gain more kinetic energy and as the friction is same, it will travel more distance??????

And; my gravity test is a kind of scale (suspended coins), why wouldn't it work?

Perhaps gold is heavier than lead. But, comon, we have to respect what Galileo had found and described some 400 years ago. In absense friction, objects fall at the same rate regardless of their weight.

[Prime]

Bad luck about proving it... Just grab three bags and make a run for it... chances are small that you would grab the bag with the fake coins... and who would care with 2 more bags of gold on board!!!!!

Just my way of saying... I have no &*%$%%& idea...! Whoops think I swore then... sorry

Better yet. Drop couple bags from the 10th floor down on the street. Go out, and pick them up. If security stops you -- you were conducting tests to find fake coins. Just carrying out your assignment, you are in no way culpable of any wrongdoing. And if they ask why you headed for the train station with those bags -- that's because you thought to find functioning scales there.

[Guest]

But is the friction the same? The friction surely varies with the amount of force appleied between the two surfaces, and the heavier coin will be pushing down harder on the table creating more friction... just like pushing the brake harder slows you down quicker cos more friction is created.

You're right about friction. But when saying friction, I aimed the forces that will stop the coin from rolling. I suppose air resistance plays more role in that force. And it isn't related with weight. Thus, although the friction is not same, rolling method should work because if you try, a table tennis ball always will roll less than an identical shaped iron ball.

[Guest]

Well, if the office has bags of coins in it, then chances are, there are more bags available. I would take a number of coins (lets say 25) out of each bag, putting them in 3 seperate bags. Given that the fake ones weight more, then 2 of the bags would feel the same weight, and one heavier. An individual coin would not be enough of a difference to feel, but a larger amount of coins would. Thats one way to find out.

Another would be to take one coin from each bag and spin them. I admit I don;t know the math and all, but I do know that the speed/length of time of a coin spinning is effected by the weight of the coin. So, two coins would spin the same, while the other would not.

Take a coin from each bag and drop it down the elevator shaft. Time the fall of each coin. The one that hits the ground fastest is heavier, and thus fake. Given that it is a summer night (morning actually, since it's 3AM) it is likely to be warm, so the sound will travel better, plus it's 3AM, no on should be there, so less noise to distract.

Thats all I can think of. And I can't find anything on the math for my second answer..

1. Not convinced you could tell the difference when you put 25 coins together verses a single coin. (relative)

#2 I like your spin idea. It should work but how would you control the spin?

#3. I agree and it is one my original answers.

[Guest]

1. Drop coins down elevator shaft. Heavier coins will land first (most of the time). For the purest repeat until you have statistical certainty.

2. Use elastic bands. Wrap a group of coins and measure stretch.

3. Create a rudimentory balance scale. ie: Book/clip board balance on glue bottle etc.

OTHERS:

4. Elevate the board room table and slide coins. Heavier coins should slide further. Prob may be the the distance may very small. I would prefer to measure the time it takes to drop off the table.

5. I really like the water scale. Fill paper cup with 10 coins and see how much it sinks.

[Guest]

You are in an office on the 10th floor of a building. It is 3 am on quiet summer night. There are ten bags filled with lots of gold coins. One of the bags is filled with faked gold coins. They are identical to the real ones except they weigh slightly more. You may not leave the office until you find three ways (at least) to determine which bag had fake gold coins.

assume normal office supplies, MacGyver.

* oh the scale you had planned use is broken.

** as a rookie not sure if this truely constitutes a puzzle but I hope it is of some interest.

1. Wait until the morning and post the puzzle on BrainDen and sit back and wait to reap the rewards.

2. Sit one coin from each bag on the radiator until they are all heated. The one which cools the quickest/slowest will be the fake.

3. Build a rudimentary catapult from a ruler and elastic bands. Shoot a coin from each bag out of the window trying to keep each shot the same. One should fall far closer or further away from the building. This method will destinguish each coins mass instead of weigh, which simply dropping it wont.

4. Copy the impulse test they do in space. 10 coins taped together to the end of a ruler. Ruler lodged sideways inbetween two desks. The time it takes for the wobbling ruler to return to rest is dependant on the mass of the coins. One set of coins will have a longer or shorter time for the ruler to return to rest.

5. Indesciminately smash the coins and the ones with chocolate inside are gold!

[Guest]

Use your staple remover to "bite" a coin from each bag. Few metals are as soft as gold.

If they're all soft, give them each a scratch with a letter opener to check for paint/plating.

If that is fruitless, simply use the floating in water in a paper cup method. Whichever bunch of coins floats at a different level than the rest is the fake.

[Guest]

Use your staple remover to "bite" a coin from each bag. Few metals are as soft as gold.

If they're all soft, give them each a scratch with a letter opener to check for paint/plating.

If that is fruitless, simply use the floating in water in a paper cup method. Whichever bunch of coins floats at a different level than the rest is the fake.

One out of three aint bad. The coins are identical except for weight. For the purest this cannot be accomplished but there are many alloys and metallurgic methods that would be able to simulate. So softness test is not within the parameters.

[Guest]

I mentioed at least three: how about. Fix a point say a jammed stapler or tack. Use the weight of a number of coins placed on top to pierce paper. Depth (number of paper) pierce should indicate heavier coins.

Could also attempt to break glass. Not sure if we can assume enough glass in an office but energy released from heavier items will cause greater damage fracture. You would need to control energy likely by dropping from a consistant height.

You are in an office on the 10th floor of a building. It is 3 am on quiet summer night. There are ten bags filled with lots of gold coins. One of the bags is filled with faked gold coins. They are identical to the real ones except they weigh slightly more. You may not leave the office until you find three ways (at least) to determine which bag had fake gold coins.

assume normal office supplies, MacGyver.

* oh the scale you had planned use is broken.

** as a rookie not sure if this truely constitutes a puzzle but I hope it is of some interest.

[bonanova]

1. Drop down elevator shaft; fakes land first. Works due to air resistance.
   
2. Rubber band. Fakes stretch more; works.
   
3. Roll the coins down a ramp. Equal time; depends on coin geometry, not density. Doesn't work.
   
4. Roll the coins down a ramp, let them coast. Fake ones will roll farther. Works. [Pinewod Derby problem]
   
5. Drop in front of vent, throw them out a window. Deflection is different due to air resistance. Works.
   
6. Float coins in a cup. Fakes sink more. Works.
   
7. Tape to ruler wedged between desks. Restoring force independent of mass. Fakes vibrate more slowly. Works.
   
8. Bite coin; grab with staple remover; break glass by dropping. Depends on hardness of material. May or may not work.
   
9. Push tack through paper. Fakes punch thru first. Works.
   

Not suggested:

1. Make pendulum, measure frequency. Depends only on length. Different from 7. Does not work.
   
2. Make pendulum, measure persistence. Real coins swing for shorter time due to air resistence. Works.
   

[Prime]

I am going to pick an issue with dropping coins down the elevator shaft. It is wrong on many levels.

The 10-story elevator shaft is about 30 meters deep. Neglecting the air resistance the dropped coin would accelerate to approximately 24 m/sec before hitting the ground. (That is using d = gt²/2 formula I've been believing in for so many years. Where g=9.8m/sec²). That's like 87 km/hr, or less than 55 miles/hr. And that's the top speed at the very end of the fall.

When I am on my bike, the wind does not bother me until about 70 mi/hr, or 110 km/hr. And gold coin's weight to its surface area ratio is so much greater than mine. Those coins are not going to notice any air resistance from such small height and will take same amount of time to fall. You are not going to see any appreciable difference. And if you could measure any time difference, it still would be inconclusive, since you cannot account for how many flips in the air the coin made before hitting the ground.

The bike analogy is the best I can do, since I never got around to learn how to calculate air resistance.

More importantly, how are you going to dig the coins out from the elevator shaft afterwards? If some coins end up missing, you'd be held accountable.

[bonanova]

I think your issue is well taken, within the confines of the OP.

It would require very precise measurement to tell the difference in fall time due to weight difference.

The methods I said would work were those for which even a possibly imperceptible difference occurs.

Drop the coins in an elevator shaft filled with water, tho, and the difference is more easily seen.

I said a method worked when there was a direct effect of density on the proposed observation.

I also postulated a measurement apparatus that had sufficient precision to detect it.

I said a method would not work when there was no direct effect by density on the proposed observation.

For example, making a pendulum and observing the period. Only the length of the string matters there.

In your cycling experience, I'm sure the drag at 70 mph is noticeable. And for your safety I hope you wear a helmet.

For competitive purposes cycling helmets [and body positions] are studied carefully for air resistance.

Electronic timers are sufficiently precise to measure the effect on arrival time when those matters are ignored, even for lesser speeds.

But the OP did not place such sensitive instruments at our disposal.

[Prime]

...

In your cycling experience, I'm sure the drag at 70 mph is noticeable. And for your safety I hope you wear a helmet.

For competitive purposes cycling helmets [and body positions] are studied carefully for air resistance.

Electronic timers are sufficiently precise to measure the effect on arrival time when those matters are ignored, even for lesser speeds.

...

To clarify: When I said "bike", I meant motorcycle, of course. No one goes 70 mph on a bicycle. Professional bicycle racers average around 30 mph over the short distances in time trials.

I have a windshield which reaches about to my chin. Without that I used to get tired of the wind hitting in my chest over the longer trips. At 75 mph or more the wind noticeably pushes my head back. And, if I don't wear a helmet, my cheeks pull back and flap in the wind. That looks ridiculous, so I usually wear a 3/4 helmet with shield, if I plan to go fast.

In case of a falling coin, when it has its edge pointing to the ground, the wind resistance is less. When it's face pointing down, the wind resistance is more. The difference in weight between fake coin and the gold one being small, the number of flips and position of the falling coin is going to be the deciding factor.

I got an impression (maybe wrong) that some posters here beleived that heavier objects fall faster in the absence of the friction/air resistance. That is not what I was brought up to believe.

[Guest]

Old gold coins were made from 'pure' gold

The only metals of sufficient density that could be used to make a fake platinum coin of the correct specifications are osmium and iridium. Produced in small quantities as a by-product of platinum, they are extremely hard, brittle metals which crumble to a powder if worked cold. They are both expensive and hard to obtain.

TEST 0ne - Counter balance using ruler

TEST Two - Mesure.There would be a difference

TEST Three - try destruction, The comparable metals for weight of gold are platinum based or tungsten. Platinum based (osmium and irridium) crrumble if worked in a cold state, tungsen is far stronger, so they destroy easily or not depending on method but very differently from gold.

I think it unlikely that gold will be faked with these metals for commen gold coins (eg kruggerands) that are weight value as oppesed to rare value

If trying to fake the more common gold coins then the cheaper heavy metals could be visible by eye comparrison (TEST Four)

Is 'the office' THE building, or A room ??? IF room, then you can not go to lift shaft, If building then you can not go outside OP says you cant leave the office

[Guest]

Old gold coins were made from 'pure' gold

The only metals of sufficient density that could be used to make a fake platinum coin of the correct specifications are osmium and iridium. Produced in small quantities as a by-product of platinum, they are extremely hard, brittle metals which crumble to a powder if worked cold. They are both expensive and hard to obtain.

TEST 0ne - Counter balance using ruler

TEST Two - Mesure.There would be a difference

TEST Three - try destruction, The comparable metals for weight of gold are platinum based or tungsten. Platinum based (osmium and irridium) crrumble if worked in a cold state, tungsen is far stronger, so they destroy easily or not depending on method but very differently from gold.

I think it unlikely that gold will be faked with these metals for commen gold coins (eg kruggerands) that are weight value as oppesed to rare value

If trying to fake the more common gold coins then the cheaper heavy metals could be visible by eye comparrison (TEST Four)

Is 'the office' THE building, or A room ??? IF room, then you can not go to lift shaft, If building then you can not go outside OP says you cant leave the office

On the Planet Xeno there is a metal(element) that has yet to be discovered. Amazingly enough it has all the properties of gold except density. Also there are methods to simulate gold using a combination of metals. In this case a destructive test would likely work but the parameters were identical except for weight.

#2 How/what were you measuring?

[Guest]

To clarify: When I said "bike", I meant motorcycle, of course. No one goes 70 mph on a bicycle. Professional bicycle racers average around 30 mph over the short distances in time trials.

I have a windshield which reaches about to my chin. Without that I used to get tired of the wind hitting in my chest over the longer trips. At 75 mph or more the wind noticeably pushes my head back. And, if I don't wear a helmet, my cheeks pull back and flap in the wind. That looks ridiculous, so I usually wear a 3/4 helmet with shield, if I plan to go fast.

In case of a falling coin, when it has its edge pointing to the ground, the wind resistance is less. When it's face pointing down, the wind resistance is more. The difference in weight between fake coin and the gold one being small, the number of flips and position of the falling coin is going to be the deciding factor.

I got an impression (maybe wrong) that some posters here beleived that heavier objects fall faster in the absence of the friction/air resistance. That is not what I was brought up to believe.

Are we saying that identical objects only with a different mass will fall at different rates when subjected to drag? This would mean that drag is a function of mass, and would be surprising to me, however I am not opposed to being surprised!

[Guest]

Give the coins to your wife/girlfriend. I tried to give mine a very realistic "gold" ring. It took her a nano second to establish that it wasn't real. This method also works if you ever find yourself in an office full of bags of diamonds.

[Prime]

Are we saying that identical objects only with a different mass will fall at different rates when subjected to drag? This would mean that drag is a function of mass, and would be surprising to me, however I am not opposed to being surprised!

I am not sure I understand your point. In presence of significant air resistance (drag) the heavier object will fall faster than the lighter object of the same shape.

Take a large coin and cut out an identical shape from a piece of Styrofoam. Drop them from the same height at the same time and observe.

Force of gravitational attraction is directly proportional to the mass of the object. F = mg, where acceleration constant g = 9.8 m/sec². In the absence of air resistance, the objects fall at the same rate (increase in attraction force being cancelled by the increase in mass g = F/m). However, it would take proportionally smaller drag force to negate gravitational attraction and reach its terminal velocity for the lighter object. In other words, while the drag force is the same for the identical shape objects moving at the same speed, smaller force is required to stop lighter object’s acceleration.