# The Naked Scientists Forum

### Author Topic: Try solving these easy problems by deductive thinking  (Read 45080 times)

#### lyner

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« Reply #50 on: 16/07/2008 23:10:23 »
I suppose it could have been a sawing horse - so no problem, again.

#### paul.fr

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« Reply #51 on: 17/07/2008 00:36:02 »
The horse was standing next to some hay in the first place, there were two bundles, but where were the oats? Did the horse have his oats?

Ok, I have thought of a picture.
« Last Edit: 17/07/2008 00:39:02 by Paul. »

#### Pumblechook

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« Reply #52 on: 17/07/2008 12:39:59 »
Two glasses, one nearly filled with liquid A, one with liquid B.  Take a teaspoon of A and put it in B, stir and put a teaspoon of the mixture back in A.   Which now is the purest??

#### BenV

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« Reply #53 on: 17/07/2008 15:54:51 »
Okay, lets get back to the pumpkins...

Quote
Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also integers. How much does each pumpkin weigh?

So, there are 5 pumpkins - lets call them a, b, c, d and e, and assume they are in ascending weight order.

And they're weighed in pairs:
a+b, a+c, a+d, a+e, b+c, b+d, b+e, c+d, c+e and d+e

This means that each pumpkin was weighed 4 times, and so the total of all the weighings/4 is the total weight of all 5 pumpkins
16+18+19+20+21+22+23+24+26+27 = 216 ... 216/4 = 54lbs

Now, if a and b are the smallest, then a+b = 16lbs
If d and e are the largest, then d+e = 27 lbs
So 54lb - (a+b)+(d+e) = c
54 - (16+27) = 11

So pumpkin c weighs 11lb.

And from there, it should be relatively easy to work out all the other weights:

a+b = 16
a+c = 18 (and therefore a= 7lb, and b=9lb)
a+d = 19 (and therefore d= 12lb)
...
d+e = 27 (and therefore e=15lb)

So:
a= 7lb
b= 9lb
c= 11lb
d= 12lb
e= 15lb

How's that?

#### BenV

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« Reply #54 on: 17/07/2008 16:04:05 »
Two glasses, one nearly filled with liquid A, one with liquid B.  Take a teaspoon of A and put it in B, stir and put a teaspoon of the mixture back in A.   Which now is the purest??
I'm going straight for the obvious answer(s), which may land me in trouble, but:

i - After all the stirring, you would have glass A with just under a teaspoon of B in, and glass B with just under a teaspoon of A in, so they're both pretty much equal

ii - neither of them are pure anymore...

Ah Ha! I've spotted the trap!  You're adding 5ml of A to a full glass of B, then 5ml of B(+A) to a glass of A minus 5 ml.  So is B more pure?

I've lost my train of thought now...

#### Pumblechook

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« Reply #55 on: 17/07/2008 18:27:30 »
It is not B.

#### Bored chemist

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« Reply #56 on: 17/07/2008 19:18:09 »
It's not A either. (I'm assuming that the volumes of the 2 liquids were identical originally.)
Unless, of course, something odd happens.
There's the complication that mixing liquids can give rise to a change in volume. Mixing a litre of alcohol with a litre of water doesn't give 2 litres of the mixture.

Otherwise, given that both glasses start and end with the same volume and that whatever is gained by one must have been lost from the other the concentration aof A in B must be the same as the concentration of B in A.

#### Alan McDougall

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« Reply #57 on: 18/07/2008 04:51:42 »
Benv,

Quote
So, there are 5 pumpkins - lets call them a, b, c, d and e, and assume they are in ascending weight order.

And they're weighed in pairs:
a+b, a+c, a+d, a+e, b+c, b+d, b+e, c+d, c+e and d+e

This means that each pumpkin was weighed 4 times, and so the total of all the weighings/4 is the total weight of all 5 pumpkins
16+18+19+20+21+22+23+24+26+27 = 216 ... 216/4 = 54lbs

Now, if a and b are the smallest, then a+b = 16lbs

If d and e are the largest, then d+e = 27 lbs
So 54lb - (a+b)+(d+e) = c
54 - (16+27) = 11

So pumpkin c weighs 11lb.

And from there, it should be relatively easy to work out all the other weights:

a+b = 16
a+c = 18 (and therefore a= 7lb, and b=9lb)
a+d = 19 (and therefore d= 12lb)
...
d+e = 27 (and therefore e=15lb)

So:
a= 7lb
b= 9lb
c= 11lb
d= 12lb
e= 15lb

"Correct and well thought out Benv"

Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also integers. How much does each pumpkin weigh

The answer is 7, 9, 11, 12, and 15 pounds.
Thanks to Elizabeth Gomez for this problem.

And thank BenV

Regards

Alan
« Last Edit: 18/07/2008 04:55:39 by Alan McDougall »

#### Alan McDougall

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« Reply #58 on: 18/07/2008 08:56:00 »
Some more problems that I think are more fun to solve!!

1) The Three Suspects
Kyle, Neal, and Grant were rounded up by their mother yesterday, because one of them was suspected of having grabbed a few too many cookies from the cookie jar. The three brothers made the following statements under very intensive questioning:
•   Kyle: I'm innocent.
•   Neal: I'm innocent.
•   Grant: Neal is the guilty one.

If only one of these statements was true, who took the cookies?

2) The Three Switches

In your basement are three light switches, all of them currently in the OFF position. Each switch controls one of three different lamps on the floor above.

You would like to find out which light switch corresponds to which lamp.
You may move turn on any of the switches any number of times, but you may only go upstairs to inspect the lamps just once.

How can you determine the switch for each lamp with just one trip upstairs?

3) The Girls, the Balls, and the Boxes

Four girls were blindfolded and each was given an identical box, containing different colored balls.
One box contained 3 black balls.
One box contained 2 black balls and 1 white ball.
One box contained 1 black ball and 2 white balls.
One box contained 3 white balls.

Each box had a label on it reading "BBB" (Three Black) or "BBW" (Two Black,
One White) or "BWW" (One Black, Two White) or "WWW" (Three White).
The girls were told that none of the four labels correctly described the contents of the box to which it was attached.
Each girl was told to draw two balls from her box, at which point the blindfold would be removed so that she could see the two balls in her hand and the label on the box assigned to her. She was given the task of trying to guess the color of the ball remaining in her box.

As each girl drew balls from her box, her colors were announced for all the girls to hear but the girls could not see the labels on any boxes other than their own.

The first girl, having drawn two black balls, looked at her label and announced: "I know the color of the third ball!"
The second girl drew one white and one black ball, looked at her label and similarly stated: "I too know the color of the third ball!"

The third girl withdrew two white balls, looked at her label, and said: "I can't tell the color of the third ball."
Finally, the fourth girl declared: "I don't need to remove my blindfold or any balls from my box, and yet I know the color of all three of them. What's more, I know the color of the third ball in each of the other boxes, as well as the labels of each of the boxes that you have."

The first three girls were amazed by the fourth girl's assertion and promptly challenged her. She proceeded to identify everything that she said she could.

Can you do the same?

Regards

Alan

#### BenV

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« Reply #59 on: 18/07/2008 10:23:53 »
Quote
The Three Suspects
Kyle, Neal, and Grant were rounded up by their mother yesterday, because one of them was suspected of having grabbed a few too many cookies from the cookie jar. The three brothers made the following statements under very intensive questioning:
•   Kyle: I'm innocent.
•   Neal: I'm innocent.
•   Grant: Neal is the guilty one.

Okay...
If Kyle is telling the truth, then Neal and Grant are lying - so Neal isn't innocent, but he is also not guilty.
If Neal is telling the truth, then Kyle and Grant are lying - so Kyle is guilty and Neal is not guilty
If Grant is telling the truth, then Kyle and Neal are guilty - so Kyle isn't innocent, and neither is Neal.

So... Neal is telling the truth, Kyle nicked the cookies and Grant, the little snitch, didn't do anything.

#### LeeE

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« Reply #60 on: 18/07/2008 15:26:45 »
A slightly quicker way to establishing Neal's innocence, without working out all the possibilities is that because Kyle's and Neal's statements are identical, one of them must be telling a lie and the other must be telling the truth.  This means Grant's statement must be untrue and therefore identifies which one is telling the lie.

#### Alan McDougall

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« Reply #61 on: 19/07/2008 08:26:02 »
Greetings

Benv,

1) The Three Suspects

Assume Neal took the cookies. If so, then both Kyle's and Grant's statements would be true. Hence it was not Neal.

Now assume Grant took the cookies. If so, then both Kyle's and Neal's statements would be true. Hence it was not Grant.

Now assume it was Kyle. This works...

"only Neal's statement was true"

#### Pumblechook

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« Reply #62 on: 19/07/2008 10:19:52 »
Three switches.   If the lamps are of a type which gets warm...............

One on.

One off.

One on for a minute or so.

Could even do 4..  One on for several miniutes..  One on for 30 secs..

Bit like when detectives want to know if a car has been driven very recently..  The engine and exhaust will be hot.

#### Alan McDougall

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« Reply #63 on: 19/07/2008 19:17:06 »
Pumblechook

Quote
Three switches.   If the lamps are of a type which gets warm...............

One on.

One off.

One on for a minute or so.

Could even do 4..  One on for several miniutes..  One on for 30 secs..

Bit like when detectives want to know if a car has been driven very recently..  The engine and exhaust will be hot.

Good solution correct

Solved in much the same way!

The Three Switches

Turn Switch 1 on and leave it on for a little while... about five minutes or more... and then turn it off.

Turn Switch 2 on and go upstairs to inspect the lamps.

The lamp with the bulb that is off but warm is controlled by Switch 1.

The lamp that is currently on is controlled by Switch 2.

The lamp that is off and cold is controlled by Switch 3

Regards

Alan

#### Alan McDougall

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« Reply #64 on: 21/07/2008 10:06:03 »
This from a free net site but wont give the link yet (no copyright)

“ Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god.

The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which. ”

These the the clarifications

“ It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)

Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

Give it I go I will try without looking at the solution

Alan

#### Alan McDougall

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« Reply #65 on: 21/07/2008 13:57:20 »
GUYS
AND GIRLS,

Here is a much easier puzzle I promise,

It doesn't hurt to take a hard look at yourself from time to time. This little test should help you get started.

During a visit to a mental asylum, a visitor asked the Director what the criteria is that defines if a patient should be institutionalized.

"Well," said the Director, "we fill up a bathtub. Then we offer a teaspoon, a teacup, and a bucket to the patient and ask the patient to empty the bathtub."

1. Would you use the spoon?
2. Would you use the teacup?
3. Would you use the bucket?

"Oh, I understand," said the visitor. "A normal person would choose the bucket, as it is larger than the spoon."
What was the director's response?

#### lyner

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« Reply #66 on: 21/07/2008 15:24:40 »
Are you allowed to pull out the bathplug?
Did he lock up the visitor?
If he did, he would soon have his institution full of visitors.

#### Bored chemist

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« Reply #67 on: 21/07/2008 18:54:56 »
I can't help thinking that a normal person would tell the director to get lost.

#### lyner

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« Reply #68 on: 22/07/2008 09:29:03 »
Or ask for some soap and a towel?

#### Alan McDougall

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« Reply #69 on: 22/07/2008 10:46:52 »
sophiec,

Quote
Are you allowed to pull out the bathplug?
Did he lock up the visitor?
If he did, he would soon have his institution full of visitors

Yes Sophie silly little puzzle was it not

#### Alan McDougall

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« Reply #70 on: 22/07/2008 10:48:22 »
Here is another easy one

A man is trapped in a room. The room has only two possible exits: two doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon.

How does the man escape?
« Last Edit: 23/07/2008 00:52:07 by Alan McDougall »

#### Alan McDougall

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« Reply #71 on: 22/07/2008 10:52:21 »
Another more based on astronomy

You awake inside a small transparent capsule sitting on the surface of Venus. From a small speaker you hear a voice that says, "We will leave you here either for a day or a year. If you choose to stay a day, we will give you \$1 million.

If you choose to stay a year, we will give you \$2 million.

Either way, you will have sufficient food and water. We will make sure the temperature is a constant 70 degrees Fahrenheit. We will also supply cable TV."

#### LeeE

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« Reply #72 on: 22/07/2008 18:18:45 »
Here is another east one

A man is trapped in a room. The room has only two possible exits: two doors. Through the first door there is a room constructed from magnifying glass. The blazing hot sun instantly fries anything or anyone that enters. Through the second door there is a fire-breathing dragon.

How does the man escape?

He waits until night time and either just walks out through the now darkened magnifying glass room, or tip-toes past the sleeping dragon.

#### LeeE

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« Reply #73 on: 22/07/2008 18:29:37 »
Another more based on astronomy

You awake inside a small transparent capsule sitting on the surface of Venus. From a small speaker you hear a voice that says, "We will leave you here either for a day or a year. If you choose to stay a day, we will give you \$1 million.

If you choose to stay a year, we will give you \$2 million.

Either way, you will have sufficient food and water. We will make sure the temperature is a constant 70 degrees Fahrenheit. We will also supply cable TV."

Is that a sidereal day or a solar day?  I'd stay for the year, as it's shorter than the sidereal day (but longer than the solar day).

#### Alan McDougall

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« Reply #74 on: 23/07/2008 00:56:45 »
LeeE

Both the anwers you gave are correct, on Venus the day is longer than the year.

The puzzle about the three gods is, however very difficult.

Alan

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« Reply #74 on: 23/07/2008 00:56:45 »