Puzzle Corner

Hint:

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There are two pans on a balancing scale.

Patience for the spouse's answer.

[Laird]

Hint:

Ah. That adds a different flavour... will think on it overnight...

Patience for the spouse's answer.

OK...

Show contentMy solution:

Six weights: 20, 10, 5, 2, 2, and 1.

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Laird, I don't think you need the 1 pound weight; just the 20, 10, 5, and 2 2's. You can create the following weights (maybe more, but they aren't needed) from the five weights:

2,4,5,7,9,10,12,14,15,17,19,20,22,24,25,27,29,30,32,34,35,37,39

Thus, there is no product weight between 1 and 40 pounds (presuming all weights are in integers) that we can't isolate from those 5 weights.  Right?

Now, getting down to 4, let alone 1, has me stumped at the moment!

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Laird, I don't think you need the 1 pound weight; just the 20, 10, 5, and 2 2's. You can create the following weights (maybe more, but they aren't needed) from the five weights:

2,4,5,7,9,10,12,14,15,17,19,20,22,24,25,27,29,30,32,34,35,37,39

Thus, there is no product weight between 1 and 40 pounds (presuming all weights are in integers) that we can't isolate from those 5 weights.  Right?

Now, getting down to 4, let alone 1, has me stumped at the moment!

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Silence, you can't assume the weights are in integers. Sorry.

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Silence, you can't assume the weights are in integers. Sorry.

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So if something weighed, say 1.56 pounds the expectation is I would able to properly round it to the "nearest 1 pound increment" of 2?

Show contentAnswer:

Maybe I'm just being silly here, but surely this fellow can do it with just 1 x 1g weight?

Ahh, patience is so under appreciated

 

Edit: Actually, rereading the original question and the specific way it is worded, my answer is the only possible, reasonable answer, unless I have completely misunderstood the question....

Well now I am curious! Is this not the right answer, Linda?  the responses are intriguing me, so I must consider I have wildly misunderstood the question, as this seems like the obvious answer?

Further spoiler speculations below! 

Show content3rd time lucky:

Right, I've now lost a long comment twice....lesson is, don't insert smiley faces into the spoiler box! Much abbreviated response:

The only valid answer is one 1g weight, as the merchant's only stated requirements are to reduce costs on weights. No mention is made of weighing all 40g in one go.

However, if I read too much into the question and make the presumption they want to weigh 40g in one go with only 4 weeights, I guess at 1g, 1g, 5g and 20g. To get to 40g, weigh 20g then replace the weight with more "product" and you have 40g total. I'm guessing all integers 1-40g can be achieved this way?

Btw, my original 2 responses were far more witty and eloquent

I realise I have far too much time on my hands........

EDIT: It's quite infurianting that I managed to unintentionally manually insert a smiley face into that response.....

Well now I am curious! Is this not the right answer, Linda?  the responses are intriguing me, so I must consider I have wildly misunderstood the question, as this seems like the obvious answer?

Further spoiler speculations below! 

Show content3rd time lucky:

Right, I've now lost a long comment twice....lesson is, don't insert smiley faces into the spoiler box! Much abbreviated response:

The only valid answer is one 1g weight, as the merchant's only stated requirements are to reduce costs on weights. No mention is made of weighing all 40g in one go.

However, if I read too much into the question and make the presumption they want to weigh 40g in one go with only 4 weeights, I guess at 1g, 1g, 5g and 20g. To get to 40g, weigh 20g then replace the weight with more "product" and you have 40g total. I'm guessing all integers 1-40g can be achieved this way?

Btw, my original 2 responses were far more witty and eloquent

I realise I have far too much time on my hands........

EDIT: It's quite infurianting that I managed to unintentionally manually insert a smiley face into that response.....

To be honest, I wasn't quite sure that I understood your response the first time. You've clarified it. 

You are correct that I didn't mention weighing it in one go, but for the sake of the puzzle, assume that it is weighed in one go. Thanks for picking up on that omission.

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You are partway there for the spouse's response.

Hold on, I just realise my secondary answer above is actually incoherent. Slightly more considered answer below:

Show content3rd answer!:

The highest weight you'd need is, actually, 10g. Weigh 10g, put product on top of weight, weigh 20g product on other side. Remove 10g weight and replace with 10g product and you have 40g total. So, revised answer - 1g, 2g, 5g and 10g. Using combinations of these weights you can reach all integers 1-40g in one weihing, albeit including moving weights or products from one scale to another, or adding weights to one scale etc.

IS THIS THE ANSWER TELL ME BEFORE I GO INSANE!!??

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So if something weighed, say 1.56 pounds the expectation is I would able to properly round it to the "nearest 1 pound increment" of 2?

The expectation is that either the weight of the product only comes in 1 pound increments, or that the weight of the product is altered to adhere to 1 pound increments. I didn't specify the product because the answer should be generic - it should be applicable to any case which satisfies the initial conditions.

Hold on, I just realise my secondary answer above is actually incoherent. Slightly more considered answer below:

Show content3rd answer!:

The highest weight you'd need is, actually, 10g. Weigh 10g, put product on top of weight, weigh 20g product on other side. Remove 10g weight and replace with 10g product and you have 40g total. So, revised answer - 1g, 2g, 5g and 10g. Using combinations of these weights you can reach all integers 1-40g in one weihing, albeit including moving weights or products from one scale to another, or adding weights to one scale etc.

IS THIS THE ANSWER TELL ME BEFORE I GO INSANE!!??

Weighing in one go means you put whatever it is you want to weigh on the scale, then you add or subtract weights until it balances. 

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I wouldn't consider your description "weighing in one go", since it involves adding and subtracting product and keeping track of which product is part of the order and which is there to balance the scale. There's a simpler answer - by simpler I mean 4 weights that get you every interval from 1 to 40, and which doesn't involve adding and subtracting other product or moving the product from side to side. 

Please note that the spouse's answer is just an aside and still requires you to figure out the value of the 4 weights.