# 2 brain teasers that I am having trouble with...
**URL:** https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165
**Category:** Factual Questions
**Created:** [October 3, 2001, 12:23pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165 "2001-10-03T12:23:24Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@Patricinus\_Scriblerus](https://boards.straightdope.com/u/Patricinus_Scriblerus)
#### Post date: [October 3, 2001, 12:23pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/1 "2001-10-03T12:23:24Z")
I am having a mental block this morning. I did know the answers to these at one point but I am just not thinking straight this morning. Please help.
Question 1:
The folks who are running the Oscars have a bit of a conundrum; shortly after they received their order
of 12 solid-gold trophies to give away to outstanding movies they discovered that one of the trophies was a fake.
The trophies all look and feel the same, but they know that the fake one has a slightly different weight from the rest.
Using a balance scale, what is the minimum number of times they will have to weight the trophies in order to determine
which is the fake and whether it is lighter or heavier than the rest of the trophies?
Question 2
In addition to the trophies, the committee had also decided to give away fresh Fakeberry pies to everybody who was nominated. Unfortunately the committee member who ordered the berries was a bit too enthusiastic and the Fakeberries arrived a month sooner than required. Fakeberries are a very succulent berry, made up of 99-percent water by weight. Over the course of the month when they sat waiting to be made into pies, the berries lost water through evaporation until at the end of the month they were only 98-percent water by weight. If they weighed 1000 kilograms before evaporation, how much did they weigh afterward?
Your help is greatly appreciated
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### Author:  [@ShibbOleth](https://boards.straightdope.com/u/ShibbOleth)
#### Post date: [October 3, 2001, 12:32pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/2 "2001-10-03T12:32:29Z")
Q1: Three
1: Weigh 6 on one side and 6 on the other.
2: Whichever side is lighter, split in half and weigh again, weighing 3 on one side and 3 on the other. Reserve the other six
3: Then whichever side is lighter weigh 1 vs 1 other, putting the third aside. If the scale is balanced after this third time, then the last left is lighter than the others.
This is the minimum number of weighings. If the fake is actually heavier, which is unlikely but perhaps possible, you would have discovered this when you did the second weighing and could then do the split again with the 6 reserved in the first step. In this case it should take you 9 weighings, but now you are looking for a heavier statuette.
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### Author:  [@astorian](https://boards.straightdope.com/u/astorian)
#### Post date: [October 3, 2001, 12:35pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/3 "2001-10-03T12:35:38Z")
There are many variations on the scale puzzle… in this case, since there are 12 statues, they can find the odd one with 3 weighings.
First, put 4 Oscars on one side of the scale and 4 on the others. If the scale tips in one direction, you’ll know which group contains the odd-weighted OScar. If they balance, the odd-weighted Oscar is one of the ones you left off the scale.
NExt, go to the set of 4 that you know contains the odd-weighted Oscar. Put 2 on each side of the scale. That will tell you which of the 2 pairs contains the odd-weighted OScar.
That leaves you with two. One more weighing, and you’ll know for sure.
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### Author:  [@ShibbOleth](https://boards.straightdope.com/u/ShibbOleth)
#### Post date: [October 3, 2001, 12:38pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/4 "2001-10-03T12:38:42Z")
> [@](#):
>
> \*Originally posted by ShibbOleth \*
> Q1: Three
>
> 1: Weigh 6 on one side and 6 on the other.
>
> 2: Whichever side is lighter, split in half and weigh again, weighing 3 on one side and 3 on the other. Reserve the other six
>
> 3: Then whichever side is lighter weigh 1 vs 1 other, putting the third aside. If the scale is balanced after this third time, then the last left is lighter than the others.
>
> This is the minimum number of weighings. If the fake is actually heavier, which is unlikely but perhaps possible, you would have discovered this when you did the second weighing and could then do the split again with the 6 reserved in the first step. In this case it should take you **9** weighings, but now you are looking for a heavier statuette.
Sorry, just finishing my morning coffee. That last bit should read **4** , not nine\*. And in case it wasn’t clear, if the statuette were heavier you would have caught this on the second weighing since the scale would have been balanced.
[sub]\*I have no clue how the number 9 got in there. It’s not as if they sit next to each other on my keyboard. [/sub]
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### Author:  [@Patricinus\_Scriblerus](https://boards.straightdope.com/u/Patricinus_Scriblerus)
#### Post date: [October 3, 2001, 12:44pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/5 "2001-10-03T12:44:11Z")
What abopt the question with the pies ??
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### Author:  [@grimpixie](https://boards.straightdope.com/u/grimpixie)
#### Post date: [October 3, 2001, 12:44pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/6 "2001-10-03T12:44:43Z")
> [@](#):
>
> \*Originally posted by ShibbOleth \*
> **Q1: Three**
Actually the **minimum** is ONE, but that requires you to get lucky when you pick the first two up… As long as one of them is the fake, you’ve scored!!🙂
As to the minimum no. weighings that **garuntees** that you find the fake, I agree THREE
Gp
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### Author:  [@Rye](https://boards.straightdope.com/u/Rye)
#### Post date: [October 3, 2001, 12:45pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/7 "2001-10-03T12:45:22Z")
Get a calc. for Q2, it’s easy 😛
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### Author:  [@grimpixie](https://boards.straightdope.com/u/grimpixie)
#### Post date: [October 3, 2001, 12:47pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/8 "2001-10-03T12:47:24Z")
Q2: Surely it must be 990 kg… but what’s the trick? Is it that people answer 980 kg (98%) and forget about the 1% other matter?
😕
Gp
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### Author:  [@Patricinus\_Scriblerus](https://boards.straightdope.com/u/Patricinus_Scriblerus)
#### Post date: [October 3, 2001, 12:50pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/9 "2001-10-03T12:50:17Z")
Ok we know what the minimum to find the fake is but the questions reads as follows:
"Using a balance scale, what is the minimum number of times they will have to weight the trophies in order to determine
which is the fake and whether it is lighter or heavier than the rest of the trophies? "
HEAVIER OR LIGHTER ? DOES IT ADD EXTRA SCALINGS TO THE SOLUTION ??
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### Author:  [@Xerxes](https://boards.straightdope.com/u/Xerxes)
#### Post date: [October 3, 2001, 12:51pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/10 "2001-10-03T12:51:43Z")
500kg. (Hope I’m not about to make an idiot out of myself).
At the start of the month you have 1000kg, comprising 990kg water (99%) and 10kg solids.
At the end of the month, the one thing you know is that they are 98% water by weight.
Assuming the solid part hasn’t altered any in weight (you must make this assumption) then you can say that the solid part comprises 2% of the final (100-98).
So, 2% of the final is 10kg.
1% is 5kg
100% is 500kg.
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### Author:  [@ShibbOleth](https://boards.straightdope.com/u/ShibbOleth)
#### Post date: [October 3, 2001, 12:55pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/11 "2001-10-03T12:55:24Z")
The second question seemed too easy, so I am waiting for one of the Board’s resident math geeks to pop in and explain why it couldn’t possibly be that simple.
That and I started to worry that perhaps we’d been conned into doing **PS** ’s homework for him.
And **grimpixie** I don’t think that the number would be _quite_ 990kg, btw.
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### Author:  [@duffman](https://boards.straightdope.com/u/duffman)
#### Post date: [October 3, 2001, 12:55pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/12 "2001-10-03T12:55:30Z")
I agree with xerxes on Q2.
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### Author:  [@ShibbOleth](https://boards.straightdope.com/u/ShibbOleth)
#### Post date: [October 3, 2001, 12:58pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/13 "2001-10-03T12:58:24Z")
> [@](#):
>
> \*Originally posted by Patricinus Scriblerus \*
> \*\*Ok we know what the minimum to find the fake is but the questions reads as follows:
>
> "Using a balance scale, what is the minimum number of times they will have to weight the trophies in order to determine
> which is the fake and whether it is lighter or heavier than the rest of the trophies? "
> HEAVIER OR LIGHTER ? DOES IT ADD EXTRA SCALINGS TO THE SOLUTION ?? \*\*
Re-read my answer. It is minimum 3, maximum 4. I think it works the same way with **Astorian** ’s solution, BTW.
And this isn’t your homework, is it?
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### Author:  [@NotMrKnowItAll](https://boards.straightdope.com/u/NotMrKnowItAll)
#### Post date: [October 3, 2001, 1:01pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/14 "2001-10-03T13:01:12Z")
The weight is 500Kg Total.
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### Author:  [@NotMrKnowItAll](https://boards.straightdope.com/u/NotMrKnowItAll)
#### Post date: [October 3, 2001, 1:03pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/15 "2001-10-03T13:03:37Z")
Let M=total mass, F=mass of fruit solids, W=mass of water
M=W+F
For 99%, .99=W/M, plugging in 1000kg for M we get 990Kg for the water and 10Kg for the fruit (M=W+10)
For 98%
.98=W/(W+10), so W is 490Kg and M=500.
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### Author:  [@Patricinus\_Scriblerus](https://boards.straightdope.com/u/Patricinus_Scriblerus)
#### Post date: [October 3, 2001, 1:08pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/16 "2001-10-03T13:08:27Z")
N:o you are not doing my homework. I am a 30yr old professional that has to supply a coule of “brain teasers” for my staff this week for a small contest. I want to make sure of the answers before I go forward. Thanks for your concerns about doing “my homework” though. It’s nice to know you are looking out for the best interests of the kids.
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### Author:  [@ShibbOleth](https://boards.straightdope.com/u/ShibbOleth)
#### Post date: [October 3, 2001, 1:31pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/17 "2001-10-03T13:31:36Z")
> [@](#):
>
> \*Originally posted by Patricinus Scriblerus \*
> N:o you are not doing my homework. I am a 30yr old professional that has to supply a coule of “brain teasers” for my staff this week for a small contest. I want to make sure of the answers before I go forward. Thanks for your concerns about doing “my homework” though. It’s nice to know you are looking out for the best interests of the kids.
No offense intended, it does happen here more often than you would think.
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### Author:  [@Sublight](https://boards.straightdope.com/u/Sublight)
#### Post date: [October 3, 2001, 1:33pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/18 "2001-10-03T13:33:39Z")
I think you’d like the book _The Chicken From Minsk_, by Yuri Chernyak and Robert Rose. It’s full of math and physics brain teasers from a workshop class taught at MIT. Your fakeberry problem is included in it.
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### Author:  [@Patricinus\_Scriblerus](https://boards.straightdope.com/u/Patricinus_Scriblerus)
#### Post date: [October 3, 2001, 1:43pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/19 "2001-10-03T13:43:51Z")
So let me make sure that I have this :
We are all agreed that the minimum # of scalings to determine the fake statue and if it is heaver or ligher is 4 right ??
and the mass of the pie is 500
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### Author:  [@CurtC](https://boards.straightdope.com/u/CurtC)
#### Post date: [October 3, 2001, 2:17pm UTC](https://boards.straightdope.com/t/2-brain-teasers-that-i-am-having-trouble-with/85165/20 "2001-10-03T14:17:25Z")
No, the fake statue can always be found with a maximum of **three** weighings.
And **grimpixie** , one will never be enough, since even if you picked two trophies and got lucky, you still wouldn’t know whether the lighter or heavier one was the fake.
500 kg is the correct answer for #2.
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