Solve Enjoyable Enigmas with Mr.E's Challenge

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A balance scale has two weights used for weightings: 0.1 kg weight and 0.4 kg weight.
Use it to divide 18 kg of grain into two bushels of 4 kg and 14 kg.
What is the minimum number of weightings required for the task?
 
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First guess would be two.
Divide the grains into half (9 and 9kgs), take one half and divide it into half again, this gives three parts of grain of 9 kg, 4.5kg, 4.5 kg.
Add the first two (13.5kg). From the last one using two weights (0.1 and 0.4) measure out 0.5 and add it to the previous part, giving 14 and 4 kg bushels.
 
Enigman said:
First guess would be two.
Divide the grains into half (9 and 9kgs), take one half and divide it into half again, this gives three parts of grain of 9 kg, 4.5kg, 4.5 kg.
Add the first two (13.5kg). From the last one using two weights (0.1 and 0.4) measure out 0.5 and add it to the previous part, giving 14 and 4 kg bushels.
I don't see how you can make the divisions into half without using the balance.

And where's the "spoiler" tag?
 
zoobyshoe said:
I don't see how you can make the divisions into half without using the balance.

Perspective?: The OP asked for the minimum number of "weightings", and I could read that to mean "using the weights to obtain a value". The balance is a given and doesn't require weights to divide in half...
 
Hmmm... I seeEm to have read it as minimum number of weights, rather than weighing. The solution still stands though, only the number of weighings is three with number of weights
used as two.
 
TumblingDice said:
Perspective?: The OP asked for the minimum number of "weightings", and I could read that to mean "using the weights to obtain a value". The balance is a given and doesn't require weights to divide in half...
He could have meant it that way, but I don't think the word "weighting" would have been used correctly if he did.

weight·ing/ˈwādiNG/
noun
  1. allowance or adjustment made in order to take account of special circumstances or compensate for a distorting factor.

The question, if he meant it that way, should have been, "What's the minimum number of times the weights have to be used in dividing the grain into two quantities, one of 4kg and the other of 14kg."
 
Enigman said:
Hmmm... I seeEm to have read it as minimum number of weights, rather than weighing. The solution still stands though, only the number of weighings is three with number of weights
used as two.
I don't see a spoiler tag in the options now offered above the reply box. Where did you find it?

Also, when I quote your all white posts, there is nothing there unless I highlight it. It's weird.
 
Click on the "+" icon on the toolbar for the spoiler tag. I colored my post white (half-darkened circle icon) to get people's goat.
Here have yours back:
Animated_animal_billy_goat_blinking_hg_clr.gif
 
Enigman said:
Click on the "+" icon on the toolbar for the spoiler tag. I colored my post white (half-darkened circle icon) to get people's goat.
Here have yours back:
Animated_animal_billy_goat_blinking_hg_clr.gif
Thank you for my goat back. And for the location of the spoiler tag. I actually didn't realize the goat was missing, though, so you can keep it. I don't want the responsibility.
 
zoobyshoe said:
He could have meant it that way, but I don't think the word "weighting" would have been used correctly if he did. (... Yah-dee-yah-dee-yah... ) The question, if he meant it that way, should have been, "What's the minimum number of times the weights have to be used in dividing the grain into two quantities, one of 4kg and the other of 14kg."
I make allowances for people who put effort into posting/communicating in English, and make my effort to consider the context.
zoki85 said:
A balance scale has two weights used for weightings: 0.1 kg weight and 0.4 kg weight.
What do you think "weightings" implies here? What are the two weights "used for?"

I have a definition to share, too:

snob (snäb)
noun
One who has an offensive air of superiority in matters of knowledge or taste.
 
zoobyshoe said:
I don't see a spoiler tag in the options now offered above the reply box. Where did you find it?

Also, when I quote your all white posts, there is nothing there unless I highlight it. It's weird.
He's using COLOR=rgb(255, 255, 255), which makes the text pure white. When you highlight the text, it changes to the highlight color.
 
TumblingDice said:
What do you think "weightings" implies here? What are the two weights "used for?"
By weighting I meant process of determining weight. In this case we use the scale and weights.
20140102-mass-and-weight.jpg
 
Exactly, Zoki. Thank you for confirming what I read your post to mean. Enigman tweaked up the answer you were looking for, right?
 
TumblingDice said:
Exactly, Zoki. Thank you for confirming what I read your post to mean. Enigman tweaked up the answer you were looking for, right?
The following solution is pretty much the same:
Divide the 18 kg between the two pans of the scale. Remove the grain from one pan and divide the other pan's 9 kg of grain between two pans. Now we have 4.5 kg on each pan. Remove 0.5 kg from one of the pans by using both the weights on the other side. You now have 4 kg and 14 kg
 
zoki85 said:
The following solution is pretty much the same:
Divide the 18 kg between the two pans of the scale. Remove the grain from one pan and divide the other pan's 9 kg of grain between two pans. Now we have 4.5 kg on each pan. Remove 0.5 kg from one of the pans by using both the weights on the other side. You now have 4 kg and 14 kg
So, how many "weightings" have you performed here?
 
zoobyshoe said:
So, how many "weightings" have you performed here?
3
 
One more.
Suppose you have four containers: 2, 4, 5, and 9 liters. 9 liters container is full of wine.
Divide the wine into three equal portions in the fewest steps. No spilling!
 
zoki85 said:
3
That's what I count as well. So, by "weighting" you meant "weighing," and by that you meant to determine the weight of something using a balance or scale, with or without the use of dedicated, premade weights. Dividing a quantity of something into two equal parts, one side of the balance used to 'weigh' the other, still constitutes a "weighing."
 
Scrap my previous solution. This is better:

1.) Fill 4 from 9
2.) Fill 2 from 9. This leaves 3 liters in 9.
3.) Pour the 2 liters now in the 2 container into the 5.
4.) Fill 5 to the top from 4. This leaves 1 in the 4 container.
5.) Fill the 2 container from the 5. This leaves 3 in the 5 container.
6.) Pour the two container into the 4 container. The 4 container now has 3.
 
zoobyshoe said:
Scrap my previous solution. This is better:

1.) Fill 4 from 9
2.) Fill 2 from 9. This leaves 3 liters in 9.
3.) Pour the 2 liters now in the 2 container into the 5.
4.) Fill 5 to the top from 4. This leaves 1 in the 4 container.
5.) Fill the 2 container from the 5. This leaves 3 in the 5 container.
6.) Pour the two container into the 4 container. The 4 container now has 3.
Yes, these are the steps ;)
 
zoki85 said:
Yes, these are the steps ;)
Thanks!

(I was all the way down at the coffee shop when I realized my first answer had superfluous steps. I rushed back, hoping no one had posted in the meantime.)
 
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I thought this one was hard due to ambiguities that required me to calculate two separate answers. If you don't perceive any ambiguity it might be easy:

Customs Duties

Two wine merchants arrive at the gates of Paris. One has 64 and the other 20 barrels of wine. Since they have not enough money to pay the customs duties, the first pays 40 francs and five barrels of wine, and the second pays 2 barrels of wine but receives 40 francs in change.

What is the value of each barrel of wine, and what is the duty payable on it?
 
Not sure if there is catch somewhere but
64x=5y+40
20x=2y-40

Value of a barrel = 120 francs
Duty payable on a barrel = 10 francs
 
zoki85 said:
Not sure if there is catch somewhere but
64x=5y+40
20x=2y-40

Value of a barrel = 120 francs
Duty payable on a barrel = 10 francs
I think this is a perfectly viable answer. There is, however, an alternate answer.
 
Dunno, maybe they had 69 barrels and 22 barrels respectively before paying duty?
 
zoki85 said:
Dunno, maybe they had 69 barrels and 22 barrels respectively before paying duty?
No, this isn't it. The number of barrels given is exactly what they arrived at the gates of Paris with.

I'll let this sit a while and see if anyone else hits on the alternative answer.
 
Ok, my last try on it. If the barrels they are paying with are considered money and not goods, they are actually paying duty for 59 barrels and 18 barrels respectively. So the equations would be:
59x=5y+40
18x=2y-40
?
 
zoki85 said:
Ok, my last try on it. If the barrels they are paying with are considered money and not goods, they are actually paying duty for 59 barrels and 18 barrels respectively. So the equations would be:
59x=5y+40
18x=2y-40
?
So, looking at this new way, what is the value of each barrel of wine, and what is the duty payable on it?
 
zoobyshoe said:
So, looking at this new way, what is the value of each barrel of wine, and what is the duty payable on it?
That doesn't interest me anymore now if you confirm this way that was the catch;)
 

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