You have six identical coins and a pair of scales. One of the coins differs slightly in weight (too small to detect by hand). You dont know if the coin is heavier or lighter than the rest. Can you determine which coin is different from the others and whether its heavier or lighter with only three or less weightings of the scales?

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(36) Jump to unreadPost a commentShhh! Don't spoil it for others! ;-)

I wont. Anyway, I could not find the site again:thumbsup:

1: The scales balance - the odd coin must be among the two coins not on the scales

2: The scales are unbalanced - the odd coin is on the scales

If 1: Put the two coins on the scales, they will be unbalanced. Switch one of the coins for one of the other four coins. If the scales balance, the coin that you just took off is the odd coin. If the scales remain unbalanced, the coin left on the scales is the odd coin.

If 2: Switch two coins (from the heavier side, say) with the two coins not currently on the scales. If the scales balance, this means that the odd coin is among the coins you just took off the scale, and it is heavier than the other coins. If the scales remain unbalanced, the coin is still on the scale, and it is lighter than the other coins. From this you can place the two coins in question on the scales, and using your knowledge of whether the coin is lighter or heaver, you can find the odd coin.

That is probably a difficult read. It's hard to put into words.

I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).

1: The scales balance - the odd coin must be among the two coins not on the scales

2: The scales are unbalanced - the odd coin is on the scales

If 1: Put the two coins on the scales, they will be unbalanced. Switch one of the coins for one of the other four coins. If the scales balance, the coin that you just took off is the odd coin. If the scales remain unbalanced, the coin left on the scales is the odd coin.

If 2: Switch two coins (from the heavier side, say) with the two coins not currently on the scales. If the scales balance, this means that the odd coin is among the coins you just took off the scale, and it is heavier than the other coins. If the scales remain unbalanced, the coin is still on the scale, and it is lighter than the other coins. From this you can place the two coins in question on the scales, and using your knowledge of whether the coin is lighter or heaver, you can find the odd coin.

That is probably a difficult read. It's hard to put into words.

I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).

good I had the solution but didnt know how to put it into words so well done :thumbsup:

One side will be haevier than the other, take these three coins and one from the remaining three.

Split therm 2each side. If the scales remain equal, then one of the remaining two is lighter than the rest.

If the scales tilt then one of the coins is heavier than all the others, and is one of the two on that scale. The third move determines which of the two is either heavier or lighter.

Put 3 coins on one side of the scale, and 3 on the other.

Whichever side weighs less has the light coin.

So out of the 3 coins from that side, place 1 on each side of the scale. If one of them is the lighter coin the scales will show it. But if they weigh the same then the 3rd coin is the lighter one and you don't even need to weigh it.

Put 3 coins on one side of the scale, and 3 on the other.

Whichever side weighs less has the light coin.

So out of the 3 coins from that side, place 1 on each side of the scale. If one of them is the lighter coin the scales will show it. But if they weigh the same then the 3rd coin is the lighter one and you don't even need to weigh it.

The coin might be heavier tho therefore on the other side!

Put 3 coins on one side of the scale, and 3 on the other.

Whichever side weighs less has the light coin.

So out of the 3 coins from that side, place 1 on each side of the scale. If one of them is the lighter coin the scales will show it. But if they weigh the same then the 3rd coin is the lighter one and you don't even need to weigh it.

this doesn't take into account that the coin might be heavier, not lighter.

I thought I'd point that out even though I don't know the answer

I have another 'puzzle'. It's actually a question I was asked for a job interview. If you have two metal balls, identical size and mass, but one is hollow, how can you work out which is which? You don't need any tools (so to speak).

Does it make a different sound when banging it (so to speak)?

the hollow ball would be lighter.

Mass should not be confused with Weight.

Nope. I tried that in the interview, and neither ball rang at all. Ultrasonic and X ray both would work (and were suitable answers in the interview), although it's not what I'm looking for here.

Mass should not be confused with Weight.

No, they're the same mass, and assuming the same gravitational field is acting on them, they both have the same weight. Think about it.

I would have said put them in water to see which one floats but they are both metal and will sink.

I think this is quite hard actually, and not just a test of logic. You need to have some certain science/applied maths/engineering knowledge to be able to answer it, just so you know.

Care to explain?

Gawd, now your asking. I can't remember the actual physics, but it's something to do with their rotational properties. Gah, is it inertia? I just seem to remember doing this experiment many years ago. :oops:

Hollow one goes for longer?

You were pretty much right, I just asked for clarification because you could also say that the hollow sphere would lose less speed if both spheres were rolled at the same speed to start with.

Benjimoron - that works as well :thumbsup:

Hollow one goes for longer?

That's also how you tell the difference between a raw egg and a hard boiled egg. :thumbsup:

Ah. :) Thanks for the explanation. Wish I could of remembered all that instead of just remembering watching the balls rolling. :oops:

Where did I go wrong?

Where did I go wrong?

That is definitely a valid method, but it wasn't what I was looking for.

Once I'd established that the spheres were made of different materials, I was informed that they were aluminium and steel. But the spheres were coated in plastic so I couldn't tell which was which by looking.

you the the idea ! Too tired to type.

Once I'd established that the spheres were made of different materials, I was informed that they were aluminium and steel. But the spheres were coated in plastic so I couldn't tell which was which by looking.

magnet?

Or did they

onlywant a mechanical solution? I suppose that, as you got the job it was all fine anyway!I think I suggested:

Cut it in half

Ultrasonic

X Ray

Magnetism

Chemical testing (ie steel would rust)

Visual inspection (upon removal of plastic coating)

Rolling them

Testing the heat capacity

By the way, I'm sorry to have hijacked your thread Abvance! Thanks for posting the puzzle in the first place, it definitely got me thinking.