Solve Enjoyable Enigmas with Mr.E's Challenge

[zoki85]

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?

 

[Enigman]

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.

 

[zoki85]

Yes:)

 

[zoobyshoe]

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?

 

[TumblingDice]

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...

 

[Enigman]

Spoiler

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.

 

[zoobyshoe]

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."

 

[zoobyshoe]

Spoiler

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.

 

[Enigman]

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:

 

[zoobyshoe]

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:

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.

 

[TumblingDice]

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.

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.

 

[Mark44]

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.

 

[zoki85]

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.

 

[TumblingDice]

Exactly, Zoki. Thank you for confirming what I read your post to mean. Enigman tweaked up the answer you were looking for, right?

 

[zoki85]

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

 

[zoobyshoe]

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?

 

[zoki85]

So, how many "weightings" have you performed here?

3

 

[zoki85]

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!

 

[zoobyshoe]

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."

 

[zoobyshoe]

Scrap my previous solution. This is better:

Spoiler

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.

 

[zoki85]

Scrap my previous solution. This is better:

Spoiler

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 ;)

 

[zoobyshoe]

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.)

 

[zoobyshoe]

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?

 

[zoki85]

Spoiler

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

 

[zoobyshoe]

Spoiler

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.

 

[zoki85]

Spoiler

Dunno, maybe they had 69 barrels and 22 barrels respectively before paying duty?

 

[zoobyshoe]

Spoiler

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.

 

[zoki85]

Spoiler

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
?

 

[zoobyshoe]

Spoiler

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?

 

[zoki85]

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;)