BrainDrain
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#1
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You are given 12 cans of drink in completely plain cans, and each can contains 330 ml of drink, but you are told one of the cans holds a different drink than the other eleven, either there are eleven cans of diet coke and one can of original coke , or eleven cans of original coke with the other being a diet coke.
Given a set of balance scales which you are only able to use for three weighings, how can you determine which is the odd can and say whether it is a diet coke or original coke?

I need to add ..belatedly for some, you are stuck in the desert desperately in need of a drink with little time left before you kick the bucket, but can only consume the contents of the cans once the problem has been solved using the scales.
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IanDangerously
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#2
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(Original post by BrainDrain)
You are given 12 cans of drink in completely plain cans, and each can contains 330 ml of drink, but you are told one of the cans holds a different drink than the other eleven, either there are eleven cans of diet coke and one can of original coke , or eleven cans of original coke with the other being a diet coke.
Given a set of balance scales which you are only able to use for three weighings, how can you determine which is the odd can and say whether it is a diet coke or original coke?
Take the cans to the nearest sink, fill it with water and dump them in. If 11 float and one sinks then the odd one out is a regular coke. If 11 sink and one float, it's a diet coke. The scales are irrelevant.
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shawn_o1
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coke is more dense than water?
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TorpidPhil
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Use your tongue? Take a sip of them and put them to the side depending on whether they taste like diet coke or ordinary coke. Is my sense of taste better than most others? It's very easy to tell the difference between the two imo.
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TorpidPhil
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If they are all 330ml of liquid surely they weigh the same?
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Whirlwind3
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(Original post by TorpidPhil)
If they are all 330ml of liquid surely they weigh the same?
You might need precise scales but I'd think that the amount of sugar they put into regular coke could have a different weight to the amount of sweeteners or whatever they put in diet coke.
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shawn_o1
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(Original post by TorpidPhil)
If they are all 330ml of liquid surely they weigh the same?
No because the solvents in the liquid change its density
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BrainDrain
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(Original post by IanDangerously)
Take the cans to the nearest sink, fill it with water and dump them in. If 11 float and one sinks then the odd one out is a regular coke. If 11 sink and one float, it's a diet coke. The scales are irrelevant.
Good thinking batman, I knew when I posted it I would miss something out, now try solving it in the desert with only the scales to help,..... I will amend the question in case others who have minds as sharp as yours will it too easy
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Whirlwind3
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#9
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Still with the thing where the sugar in the regular coke is heavier than the sweeteners in the diet coke.
If it's those balancing scales you could put 5 on each side and if they're balanced then the other 1 is the diet?
If it isn't balanced then you take the ones of the side that is higher and put 2 on each side and keep one off. If the scales are balanced then it's the one you don't have on, if they aren't then you take the 2 remaining cans that were on the side of the scales that raised and balance them then the one which raises is the diet I guess.
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Kevin De Bruyne
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I think I've seen this problem before, in the shape of 8 coins with one fake that was slightly heavier than the others, and you are limited to 2 uses of the scales.

If you assume that the 1 diet coke is lighter, then take 5 and measure it against 5. If they're equal, just weigh the remaining 2 against eachother. If one is lighter... you can keep going and it only takes 2 more scale uses.

Edit: not quite. Maybe 4 vs 4 initially?


(Original post by BrainDrain)
Good thinking batman, I knew when I posted it I would miss something out, now try solving it in the desert with only the scales to help,..... I will amend the question in case others who have minds as sharp as yours will it too easy
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IanDangerously
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(Original post by BrainDrain)
Good thinking batman, I knew when I posted it I would miss something out, now try solving it in the desert with only the scales to help,..... I will amend the question in case others who have minds as sharp as yours will it too easy
Split the cans into four groups of 3. On the first weigh put a group each side. If it unbalances, the heavier side contains more regular coke. Take those 3 cans and weigh one against the other, if it balances now the 2 on the scales are regular and the one you're not weighing is diet. If it doesn't, the lighter one is diet and the heavier one and the unweighed one must be regular.

If it balances the first time, take one group off and put another one. Now if it unbalances repeat the step and if it doesn't, the odd can must be in the 3 you never weighed so use them as the final set.
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BrainDrain
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#12
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(Original post by BrainDrain)
You are given 12 cans of drink in completely plain cans, and each can contains 330 ml of drink, but you are told one of the cans holds a different drink than the other eleven, either there are eleven cans of diet coke and one can of original coke , or eleven cans of original coke with the other being a diet coke.
Given a set of balance scales which you are only able to use for three weighings, how can you determine which is the odd can and say whether it is a diet coke or original coke?

I need to add ..belatedly for some, you are stuck in the desert desperately in need of a drink with little time left before you kick the bucket, but can only consume the contents of the cans once the problem has been solved using the scales.


Some nice attempts guys but no cigar yet.... remember you are limited to using the balance scales only three times.
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Thorndyke
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#13
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Split the cans in to 2 groups of 6, weigh them against each other to find the lightest, or heaviest pair depending if you want diet or regular.

Once you have that group, split it in to 2 groups of 3, which you can weigh against each other the same way as before leaving you with 3 cans.

Then weigh 2 of the cans against each other, leaving 1 off of the scales at the side.

If they even out, the one you put to the side is the odd (either heavier or lighter) can

If not, just pick the heavier/lighter can.

So if you wanted to ensure you get diet when 11 regular cans are present, always go for the lighter one, and go for the heavier when 11 diet are present to get a regular can.

That's assuming that there is a weight difference of course
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