BS: Math problems

Subject: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 01:16 PM

To help get the brain cells firing. Not hard but require a bit of thought.

Problem 1: A man saves his kingdom from disaster and is brought before the king to be rewarded. The king says, "Name your reward, my good man, and I shall grant it." The man walks over to the king's chessboard and places a single grain of rice on a corner square. He then says, "If you would, sire, double the amount on each succeeding square so that the second square shall have two grains and the third shall have four grains and the fourth shall have eight and so on until all the squares are filled in." The king says, "Consider it done!"

Did the king make a wise decision? How much rice will the king require to fulfill the request?

Problem 2: Two witches are mixing a brew in a cauldron when the recipe calls for exactly 4 pints of yak sweat. They have a bucketful of yak sweat but no 4-pint measure. They have a pitcher that hold exactly 5 pints and a pot that holds exactly 3.

How can they use these to measure out the required 4 pints?

Problem 3: Millie and Geraldine are tending their flowers. One vase holds 5-petal primroses and 8-petal celandines. Millie counts all the petals and says, "Thirty-nine! Exactly my age!" Then she counts the flowers and says, "Exactly your age, Geraldine!"

How old is Geraldine?

Problem 4: Which 2-digit number is one more than a square and one less than a cube?

Problem 5: Which 3-digit number is made of consecutive digits and is two less than a cube but two more than a square?

Subject: RE: BS: Math problems
From: Jean(eanjay)
Date: 29 Apr 12 - 01:41 PM

problem 4 is 26

Subject: RE: BS: Math problems
From: Jean(eanjay)
Date: 29 Apr 12 - 01:44 PM

problem 5 is 123

Subject: RE: BS: Math problems
From: Will Fly
Date: 29 Apr 12 - 01:46 PM

The king (1) made a really stupid decision - 2 to the power of 62 is a very, very large number...

Subject: RE: BS: Math problems
From: Jean(eanjay)
Date: 29 Apr 12 - 01:50 PM

Problem 3: - if there are the same number of primroses as celandines then there are 6 flowers so Geraldine is 6 years old.

Subject: RE: BS: Math problems
From: Jean(eanjay)
Date: 29 Apr 12 - 01:55 PM

Problem2: fill the pot from a full pitcher so 2 pints are left in the pitcher ~ do this twice.

Subject: RE: BS: Math problems
From: Jean(eanjay)
Date: 29 Apr 12 - 01:57 PM

I have some maths problems that I will try to find to add to this thread.

Subject: RE: BS: Math problems
From: Will Fly
Date: 29 Apr 12 - 01:59 PM

A slightly off-topic question: Why do people in the UK call the short form of the word 'mathematics' maths, and people in the US call it math?

Just curious.

Subject: RE: BS: Math problems
From: gnu
Date: 29 Apr 12 - 02:02 PM

They are not ped. >;-)

Subject: RE: BS: Math problems
From: Jean(eanjay)
Date: 29 Apr 12 - 02:12 PM

Why do people in the UK call the short form of the word 'mathematics' maths, and people in the US call it math?

No idea :) ~ but this link is interesting:

DailyWritingTips

Subject: RE: BS: Math problems
From: gnu
Date: 29 Apr 12 - 02:20 PM

From Jean's link... "It's sometimes surprising how much argument and disagreement small differences such as that single letter can make."

No shit, Sherlock. >;-)

Subject: RE: BS: Math problems
From: Bert
Date: 29 Apr 12 - 02:31 PM

Actually, In England we used to call mathematics sums.

Subject: RE: BS: Math problems
From: Bonzo3legs
Date: 29 Apr 12 - 02:41 PM

Or we called it maths - math is plain silly!!

Subject: RE: BS: Math problems
From: Bonzo3legs
Date: 29 Apr 12 - 02:42 PM

Ah - missed the above post, but math is still silly.

Subject: RE: BS: Math problems
From: gnu
Date: 29 Apr 12 - 02:43 PM

Maybe math is short for mathematical?

Subject: RE: BS: Math problems
From: Bill D
Date: 29 Apr 12 - 02:54 PM

#1..."and so on until all the squares are filled in"

If the king is half as clever as the creator of the idea, he would take it literally and add rice until *"all the squares are filled in"*

By perhaps the 20th square, rice would spill over and make going to 64 moot.

Subject: RE: BS: Math problems
From: Bill D
Date: 29 Apr 12 - 02:56 PM

"math" is a shorthand term for a discipline. You would't say 'arithmetics'.

Subject: RE: BS: Math problems
From: Bert
Date: 29 Apr 12 - 02:57 PM

They call it math 'cos in the US there is only one of them.

Subject: RE: BS: Math problems
From: gnu
Date: 29 Apr 12 - 03:10 PM

Bill D! YOU win the prize! Engineers always beat the mathematicians. Well done.

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 03:14 PM

/////Problem2: fill the pot from a full pitcher so 2 pints are left in the pitcher ~ do this twice./////

That's far too short on specifics to be a viable solution.

Subject: RE: BS: Math problems
From: gnu
Date: 29 Apr 12 - 03:18 PM

An engineer and a math guy are lined up and told that each time a whistle is blown they may advance half of the distance toward a beautiful naked woman 100 yards away. The whistle blows and the engineer runs like crazy. The mathy stands still.

When asked why he didn't proceed, the mathy says, "If you go half the distance each whistle blow, you'll never reach the objective."

When asked why he ran like crazy, given the fact that the mathy provided, the engineer says, "For all intents and purposes, I'll get close enough."

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 03:23 PM

Persons A, B, C and D were shown a number that you didn't see but you have to deduce it.

A says, "It's two digits."
B says, "It goes evenly into 150."
C says, "It is not 150."
D says, "It's divisible by 25."

You now have all the information needed to figure out the number EXCEPT one of them is lying.

What is the number and who is lying?

Subject: RE: BS: Math problems
From: Paul Burke
Date: 29 Apr 12 - 03:46 PM

One answer would be C. But I can't be bothered working out any others.

μαθηματικός ends in 's' which might have sounded a bit like a plural in Oxbridge days. Ars mathematica would on the other hand have soundec like a bum deal.

Why don't you Yanks just call it "arse"?

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 03:53 PM

If C is lying then the number IS 150 but that would mean that A is also lying but only one person is lying.

Subject: RE: BS: Math problems
From: Paul Burke
Date: 29 Apr 12 - 04:00 PM

Three fisherman were fishing on a secluded island. The fish briskly gobbled the bait; the fisherman were so absorbed that they did not notice that night had come and did not realize till too late what a mountain of fish they had hooked. So they had to spend the night on the island. Two fisherman quickly fell asleep, each nestled down under his boat, but the third had insomnia and decided to go home. He did not wake his comrades, but divided all the fish into three parts. There proved to be one extra fish. After a moment's thought, he threw it into the water, took his hare, and went home.

In the middle of the night, the second fisherman woke up. He did not know that the first fisherman had already left and also divided all the fish into three and, as before, there was one fish left over. As before, the fisherman threw the extra fish in the water, took his share, and went home.

By early morning, the third fisherman awoke. He did not notice that the other two fisherman had left, so he too divided all the fish into three and, as before, there was one fish left over. As did his comrades before him, the fisherman threw the extra fish in the water, took his share, and went home.

Determine the least number of fish that the fisherman could have caught.

Without googling 'Dirac'.

Subject: RE: BS: Math problems
From: Jeri
Date: 29 Apr 12 - 04:04 PM

The answer is D and the number is 30.

A says, "It's two digits." The number would have to be 100 or more, and B could not be true.
B says, "It goes evenly into 150." If this is untrue, D could also not be true.
C says, "It is not 150." If this is untrue 150, or A would also not be true.

Subject: RE: BS: Math problems
From: frogprince
Date: 29 Apr 12 - 04:07 PM

Okay, problem 2: Jean actually solved it, but: fill the five pint container; fill the three pint container from the five pint; put the remaining two pints in the potion; empty the three pint container back into the bucket; fill the five pint; fill the three pint from the five pint; put the remaining two pints in the potion.

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 04:13 PM

No because when the formula calls for 4 pints, you put in 4 pints, not 2 pints now and 2 pints later. You have to have 4 pints ready to go. So how do you do it?

Subject: RE: BS: Math problems
From: Doug Chadwick
Date: 29 Apr 12 - 04:13 PM

B is lying and the number is 50

Problem 2:
Fill the 5 pint pithcher;
Fill the 3 pint pot from the pitcher, leaving 2 pints in the pitcher;
Empty the pot and transfer the 2 pints from the pitcher to the pot;
Fill the pitcher again;
Pour yak sweat from the pitcher into the 1 pint space left in the pot until it is full;
4 pints will be left in the pitcher.

Subject: RE: BS: Math problems
From: Mo the caller
Date: 29 Apr 12 - 04:14 PM

If by B 'goes evenly' you mean 150 / x is an even number, then B could be lying and the answer 50.

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 04:28 PM

////Problem 2:
Fill the 5 pint pithcher;
Fill the 3 pint pot from the pitcher, leaving 2 pints in the pitcher;
Empty the pot and transfer the 2 pints from the pitcher to the pot;
Fill the pitcher again;
Pour yak sweat from the pitcher into the 1 pint space left in the pot until it is full;
4 pints will be left in the pitcher.////

Correct although you empty the pot by pouring it back into the bucket. But you're close enough.

Subject: RE: BS: Math problems
From: gnu
Date: 29 Apr 12 - 04:40 PM

I love this stuff. As an engineering student, I was required to take a certain number of credit hours in "arts" courses. I opted for a basic philosophy course and learned the very basics/basis of human thought. Logic problems are cool when you know the basics of philosophy. Learning the basics of human reasoning is way cool.

Of course, I used to smoke pot way back in those days, so maybe it wasn't WAY cool, but I still thing it's cool stuff.

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 04:40 PM

////The answer is D and the number is 30.

A says, "It's two digits." The number would have to be 100 or more, and B could not be true.
B says, "It goes evenly into 150." If this is untrue, D could also not be true.
C says, "It is not 150." If this is untrue 150, or A would also not be true.////

Correct.

////B is lying and the number is 50/////

If B is lying then either A or D would also have to be lying and only one person is lying.

Subject: RE: BS: Math problems
From: Doug Chadwick
Date: 29 Apr 12 - 04:41 PM

....although you empty the pot by pouring it back into the bucket.


That's not very hygenic, is it? Hang the expense, fresh yak sweat every time, I say, if you're going to make a quality brew.

Subject: RE: BS: Math problems
From: DMcG
Date: 29 Apr 12 - 04:46 PM

So why is 10 not also valid?

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 04:47 PM

Ok, gnu, two robots are walking along being guided by radio signals. Robot A says to Robot B, "If I had one of your antennas, we'd have the same number."
B replies, "If I had two of your antennas, I'd have 5 times as many as you!"

How many antennas does each robot have?

Subject: RE: BS: Math problems
From: Doug Chadwick
Date: 29 Apr 12 - 04:56 PM

It goes evenly into 150

Do you actually mean: "It goes exactly into 150" (i.e. with no remainder) ?


I interpreted it the same way as Mo: "...150 / x is an even number..."    - both 30 and 50 go an odd number of times into 150.


DC

Subject: RE: BS: Math problems
From: Doug Chadwick
Date: 29 Apr 12 - 05:29 PM

The sums work out as 3.5 antennas for robot A and 5.5 for robot B but an antenna either works or it doesn't. Even if it is broken in half, a working half-antenna should count as 1 and a non-working half-antenna should count as zero.


DC

Subject: RE: BS: Math problems
From: MudGuard
Date: 29 Apr 12 - 06:13 PM

Problem 2: Two witches are mixing a brew in a cauldron when the recipe calls for exactly 4 pints of yak sweat. They have a bucketful of yak sweat but no 4-pint measure. They have a pitcher that hold exactly 5 pints and a pot that holds exactly 3.

Fill the 3-Pint-Pot from bucket, and put its content into the 5-Pint-Pitcher.
Fill the 3-Pint-Pot again from the bucket, and fill up the 5-pint-pitcher. This leaves 1 pint in the pot. Put that into the cauldron.

Fill the 3-Pint-pot from the pitcher. Empty the pitcher into the cauldron.

Now 4 pints went into the cauldron.

The remaining 2 pints in the pitcher may be poured back into the bucket.

Subject: RE: BS: Math problems
From: JohnInKansas
Date: 29 Apr 12 - 06:17 PM

While the statement is sort of a correct statement:

The king (1) made a really stupid decision - 2 to the power of 62 is a very, very large number

it isn't really "the answer."

The first difficulty is that there are 64 squares on a chessboard rather than 62, making the correct answer 2⁶⁴ - 1. (There is no argument that 2⁶² isn't a very big number.)

The quantity of rice on the first square is 2⁰ rather than 2, so the quantity on the last square is 2⁶³ grains, and the sum of them all is as indicated.

1.8446744*10¹⁹ grains, as close as my calculator can conveniently display it, (or 18,446,744,000,000,000,000 grains) which quite possibly still exceeds a century's worth of the total rice production for the entire world, as it did back when George Gamow included the problem in his book One, Two, Three, ... Infinity. (I read it ca. 1947 or so, but I think it had been around for a while then. Still a pretty good book for reasonably clever kids, or even for slightly less clever adults who might be curious.)

John

Subject: RE: BS: Math problems
From: Will Fly
Date: 29 Apr 12 - 06:34 PM

The quantity of rice on the first square is 20 rather than 2, so the quantity on the last square is 263

The quantity of rice on the first square is 1. The quantity of rice on the 2nd square is therefore 2 - leaving 62 squares of the total 64. Therefore 2 to the power of 62 - or have I missed something?

1 to the power of 64 is 1.

Subject: RE: BS: Math problems
From: JohnInKansas
Date: 29 Apr 12 - 06:35 PM

A very old problem concerns a tall building and three experts, an physicist, a mathematician, and an engineer.

Each was given a watch, a long piece of string, and a level, and was asked to determine the height of the building.

The mathematician tied the watch to the string, went to the top, and swung it like a pendulum, and calculated the length of the string from the frequency of the pendulum. His answer was off by about 10 per cent.

The physicist went to the top, read the time on the clock, and then dropped it. Comparing the time elapsed to when the clock stopped (literally) he calculated the free-fall time to deduce the height, and his answer was off by about 7 per cent.

The engineer went inside, and reappeared with the exactly correct answer.

How did he do it?

(Note: it's a bit of a trick question?)

John

Subject: RE: BS: Math problems
From: JohnInKansas
Date: 29 Apr 12 - 06:46 PM

Will -

First square 1 grain is 2⁰ grains
Second square 2 grains is 2¹ grains
Third square 4 grains is 2² grains
...
64th square is 2⁶³ grains

The sum of all of the grains on the board is 2⁶⁴ - 1 grains.

(I left the calculation of the sum as a homework problem for the students.)

John

Subject: RE: BS: Math problems
From: framus
Date: 29 Apr 12 - 08:23 PM

Surely the rice question is nothing to do with squaring, but DOUBLING the previous number?
I assume the engineer just measured the piece of string and used it to measure the distance to the building, then - oh sod it, it's 1.30 am.

Subject: RE: BS: Math problems
From: frogprince
Date: 29 Apr 12 - 09:45 PM

The engineer went to check the blueprints.

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 10:00 PM

////The sums work out as 3.5 antennas for robot A and 5.5 for robot B but an antenna either works or it doesn't. Even if it is broken in half, a working half-antenna should count as 1 and a non-working half-antenna should count as zero.////

I jacked that problem up deliberately for gnu who apparently didn't waste two seconds on it. Leave it to Doug to do it for him. And now you've paid for your insulin. Or your insolence. Or maybe both. So here we are.

By the way, your answer appears to be correct.

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 29 Apr 12 - 11:21 PM

Anybody working on that fish problem? I was doing some preliminary head calculations about it earlier. Maybe someone else went further?

Subject: RE: BS: Math problems
From: JohnInKansas
Date: 29 Apr 12 - 11:43 PM

Frogpince heard the building height story before (?).

Lest anyone waste more time on it, the "classic" answer is that the engineer gave the watch to the building janitor in exchange for a look at the blueprint.

The story has been used since at least the '50s when the prof wants to convince the engineering students that they need at least some knowledge of business to succeed.

(Not everyone believes the profs on this. It depends on what kind of engineer they want to be.)

John

Subject: RE: BS: Math problems
From: Bill D
Date: 30 Apr 12 - 12:13 AM

An old rancher died and stipulated in his will that his horses were to be divided among his 3 sons. His oldest was to get ½ the horses, his 2nd son 1/3, and the youngest son 1/9 of the horses.... but when they checked, there were 17 horses. How did the lawyer solve the problem?

Subject: RE: BS: Math problems
From: BK Lick
Date: 30 Apr 12 - 02:16 AM

Here are the first three puzzles in Chapter 1 of Raymond Smullyan's lovely book The Lady or the Tiger?:

1 • How much?
Suppose you and I have the same amount of money. How much must I give you so that you have ten dollars more than I?

2 • The Politician Puzzle
A certain convention numbered one hundred politicians. Each politician was either crooked or honest. We are given the following two facts:

(1) At least one of the politicians was honest.
(2) Given any two of the politicians, at least one of the two was crooked.

Can it be determined from these two facts how many of the politicians were honest and how many were crooked?

3 • Old Wine in a Not-so-new Bottle
A bottle of wine cost ten dollars. The wine was worth nine dollars more than the bottle. How much was the bottle worth?

Subject: RE: BS: Math problems
From: Doug Chadwick
Date: 30 Apr 12 - 04:15 AM

Anybody working on that fish problem? I was doing some preliminary head calculations about it earlier. Maybe someone else went further?


The least number of fish that the 3rd fisherman dealt with is one each plus one extra

i.e.    3 + 1 = 4

The 2nd fisherman dealt with 3 times this many plus an extra one

i.e.    3x4 + 1 = 13

The 1st fisherman dealt with 3 times this many plus an extra one

i.e.   3x13 + 1 = 40, so that is the least number of fish caught.


A second part of the problem, that could be considered, is not an exercise in logic but is subjective and based on experience. How many beers would it take for 3 guys to catch 40 fish?


DC

Subject: RE: BS: Math problems
From: Will Fly
Date: 30 Apr 12 - 05:24 AM

Hi John (in Kansas) - just checked the amount of rice using Excel and my forumla - it adds up, as you said, to 18,446,744,073,709,600,000 grains.

So, we may differ slightly as to the basis of the calculation, but the result appears to be the same! :-)

Subject: RE: BS: Math problems
From: Doug Chadwick
Date: 30 Apr 12 - 05:46 AM

The sum of all of the grains on the board is 2⁶⁴ - 1 grains

In the opening post it says that the man provided the first grain of rice himself, so the king only had to provide 2⁶⁴ - 2 grains.
Not as bad as it first seemed then!


DC

Subject: RE: BS: Math problems
From: MudGuard
Date: 30 Apr 12 - 07:51 AM

the exact number of rice grains involved is
18.446.744.073.709.551.615

Excel seems not able to handle such big numbers exactly.

Subject: RE: BS: Math problems
From: Will Fly
Date: 30 Apr 12 - 10:08 AM

Excel tends to truncate large numbers with the E+ signage - I had to force the full version with commas in the cells formatting - but still not an exact number!

Subject: RE: BS: Math problems
From: Bobert
Date: 30 Apr 12 - 10:38 AM

Child's play, ya'll!!!

So I took all the problems and turned them into one of the multi-nomial clusterfuck of problems to be solved as one problem and put it on the Wes Ginny Slide Rule... Well, half an hour later the WGSR had it figured out and the answer was...

Subject: RE: BS: Math problems
From: Bobert
Date: 30 Apr 12 - 10:39 AM

... Mitt Romney - 3...

Hey, it was so obvious...

B;~)

Subject: RE: BS: Math problems
From: Newport Boy
Date: 30 Apr 12 - 10:49 AM

An old rancher died and stipulated in his will that his horses were to be divided among his 3 sons. His oldest was to get ½ the horses, his 2nd son 1/3, and the youngest son 1/9 of the horses.... but when they checked, there were 17 horses. How did the lawyer solve the problem?

The lawyer lent them a horse, so there were 18 horses. The sons received 9 + 6 + 2 = 17 horses, and the lawyer had his horse back. The lawyer charged $100 for the loan of the horse!

Phil

Subject: RE: BS: Math problems
From: Newport Boy
Date: 30 Apr 12 - 10:51 AM

Re the fish problem, where did the first man get the hare from?

There proved to be one extra fish. After a moment's thought, he threw it into the water, took his hare, and went home.

Phil

Subject: RE: BS: Math problems
From: Bert
Date: 30 Apr 12 - 03:16 PM

If a herring and a half costs three ha'pence, how much does a dozen cost?

Subject: RE: BS: Math problems
From: GUEST,CrazyEddie
Date: 30 Apr 12 - 04:28 PM

That'd be a bob a dozen Bert, but I'll let you have half-a-dozen for a tanner.

Subject: RE: BS: Math problems
From: GUEST,Eliza
Date: 30 Apr 12 - 05:30 PM

I always thought that the plural of 'antenna' was 'antennae'.

Subject: RE: BS: Math problems
From: GUEST,Eliza
Date: 30 Apr 12 - 05:31 PM

And while we're at it, the plural of formula was formulae!

Subject: RE: BS: Math problems
From: Paul Burke
Date: 30 Apr 12 - 06:04 PM

Let's work that through Doug. 40 fish, throw one away. That's 39. 13 each, so early riser goes off with his share. That leaves 26. Throw one of those away and 25 are left, which doesn't divide evenly by 3.

79 fish works though. Thow one away = 78. Take 26, leaving 52. Next chap throws one away, leaving 51. He takes his 17, leaving 34. Lazybones throws 1 away and takes his 11, leaving 22 to rot.

Dirac's answer was much better, though I think he cheated a bit. He proposed that the number of fish caught was -2. Throw one away, that's -3. Take your third, and that leaves -2 again. Any number of fishermen could have shared the catch in this manner.

Subject: RE: BS: Math problems
From: Mr Happy
Date: 01 May 12 - 07:47 AM

.......but what of the hare, did it relope?

Subject: RE: BS: Math problems
From: Nigel Parsons
Date: 01 May 12 - 08:00 AM

I'm playing catch-up here as I'm on holiday in the Canaries (Isles of dogs, not to be confused with Canary Wharf in London which is on the area previously known as "the isle of dogs"). So:

If C is lying then the number IS 150 but that would mean that A is also lying but only one person is lying.
No, the question states " You now have all the information needed to figure out the number EXCEPT one of them is lying. it doesn't actually state that only one of them is lying! (a small point, but badly phrased questions permit multiple correct answers!)

Bert: Actually, In England we used to call mathematics sums.
Strange, in Wales we called Arithmetic 'Sums'. Mathematics (hence the plural 'maths') was the three mathematical disciplines of Arithmetic, Geometry & Algebra.

1 • How much?
Suppose you and I have the same amount of money. How much must I give you so that you have ten dollars more than I? 5 dollars

2 • The Politician Puzzle
A certain convention numbered one hundred politicians. Each politician was either crooked or honest. We are given the following two facts:
(1) At least one of the politicians was honest.
(2) Given any two of the politicians, at least one of the two was crooked.
Can it be determined from these two facts how many of the politicians were honest and how many were crooked? One honest & 99 dishonest. (We may be wrong about the one though!)

3 • Old Wine in a Not-so-new Bottle
A bottle of wine cost ten dollars. The wine was worth nine dollars more than the bottle. How much was the bottle worth? 50cents

Subject: RE: BS: Math problems
From: BK Lick
Date: 02 May 12 - 03:43 AM

"79 fish works though"

So does 25, 52, and all numbers of the form 27n - 2 where n is any integer.

For then:
Fisherman 1 leaves 2/3 (27n - 3) = 18n - 2 fish;
Fisherman 2 leaves 2/3 (18n - 3) = 12n - 2 fish;
Fisherman 3 leaves 2/3 (12n - 3) =   8n - 2 fish.

Subject: RE: BS: Math problems
From: banjoman
Date: 02 May 12 - 06:16 AM

I think that the engineer went into the building and asked the person who designed it how tall it was and gave hime the clock as a reward for the information.
New problem:
If it takes a week to walk a fortnight then how long will it take for a legless spider to crawl out of a pot of jam backwards.
Another trick question

Subject: RE: BS: Math problems
From: GUEST,CrazyEddie
Date: 02 May 12 - 07:19 AM

Nigel,
Re: One honest & 99 dishonest. (We may be wrong about the one though!).

No, he's honest alright. Unlike the others, if you buy him he STAYS bought.

Subject: RE: BS: Math problems
From: gnu
Date: 02 May 12 - 02:11 PM

How much wood could a woodchuck chuck if a woodchuck could chuck wood?

Subject: RE: BS: Math problems
From: dick greenhaus
Date: 02 May 12 - 09:08 PM

Say you have a liter of water and a liter of wine. You put one tablespoon of wine in the water, mix it, and put one tablespoon of the mixture back into the wine. Is there more water in the wine, or wine in the water?

Subject: RE: BS: Math problems
From: GUEST,josepp
Date: 03 May 12 - 12:13 AM

/////If C is lying then the number IS 150 but that would mean that A is also lying but only one person is lying.
No, the question states " You now have all the information needed to figure out the number EXCEPT one of them is lying. it doesn't actually state that only one of them is lying! (a small point, but badly phrased questions permit multiple correct answers)////

That's funny because there ARE multiple correct answers. I never said there weren't. Therefore, by your statement above, I must have worded it exactly correct. If you disagree, then you must agree that your statement above is shit.

Clear on that?

Subject: RE: BS: Math problems
From: MudGuard
Date: 05 May 12 - 03:41 PM

>> If a herring and a half costs three ha'pence, how much does a dozen cost?

about 6 times as much.
(because you get a rebate if you buy a full dozen ;-))

Subject: RE: BS: Math problems
From: Bert
Date: 05 May 12 - 05:07 PM

Dick, they are the same.

Nice one Mudguard, hadn't thought of that. Actually it is the question that is ambiguous 'cos it doesn't specify whether it is a dozen herrings or a dozen 'herring and a half's

Subject: RE: BS: Math problems
From: Paul Burke
Date: 05 May 12 - 05:08 PM

Dick's problem is an odd one, partly because wine is a mixture containing water, and partly because one component of wine- ethanol- dissolves in water such that 1 pint water + 1 pint water results in not 2 pints of mixture, but about 8% less.

Although there is "water" at one end of the scale and "wine" at the other, there is no point at which you can say that it has ceased to be water, and become wine- and vice versa. And water is never pure H2O. So one one level, the water is still water and the wine is still wine.

But let's simplify- assume no significant change in volume on mixing, and assume that the "wine" is a component that can be labelled put in a pot marked A (for Alcohol). The water is of course marked W, and we assume unit volumes W and A.

Let the size of the spoon be S (0 < S < 1). Then a spoon of wine is SA, and putting this in the water results in W+SA.

The wine is now (1-S)A.

Now take a spoonful of the mixture S(W+SA) = SW + SSA, and add it to (1-S)A = (1-S)A+SW+SSA. The result is A-SA+SW+SSA.

The remainder in the water is (1-S)(W+SA) = W-SW+SA-SSA.

The quantity of wine in the pot marked W is SA-SSA.

The quantity of water in the pot marked A is SW.

Therefore there is more (absolute quantity) of water in the wine than there is wine in the water.

You might want to go on and work out which is the greater proportion of the other.

Subject: RE: BS: Math problems
From: gnu
Date: 05 May 12 - 05:11 PM

I'll have a glass of the wine, thanks.

Subject: RE: BS: Math problems
From: Paul Burke
Date: 05 May 12 - 05:21 PM

Bollocks of course-

"1 pint water + 1 pint water results in not 2 pints of mixture, but about 8% less. " ... should be plus 1 pint alcohol

And the wine mix has lost a spoonful, so is now (1-S)(A+SA+SW+SSA) Just solve for the water = (1-S)SW = SW-SSW,

The same as A in the other pot.

Subject: RE: BS: Math problems
From: Nigel Parsons
Date: 05 May 12 - 10:10 PM

From:dick greenhaus - PM
Date: 02 May 12 - 09:08 PM

Say you have a liter of water and a liter of wine. You put one tablespoon of wine in the water, mix it, and put one tablespoon of the mixture back into the wine. Is there more water in the wine, or wine in the water?
If you start with two one litre (not liter) containers, and after messing about they still each contain one litre of liquid, then any amount transferred from A to B is matched by a similar transfer from B to A. So the total volume of the two containers remains the same. If one container holds 90+xx percent of wine, then the other container contains 90+xx percent of water.

Subject: RE: BS: Math problems
From: Jeri
Date: 05 May 12 - 10:29 PM

There's more wine in the water than water in the wine. What you added to the water was 100% wine. What you added to the wine was one tablespoon from a liter of water with one tablespoon of wine mixed in.

What you added to the water was pure wine.
What you added to the wine was water and wine.

While it's true that one tablespoon of wine was removed from the liter of wine, slightly less than a tablespoon of water was removed from the liter of water--some of it was wine that got put back into the liter of wine.

Subject: RE: BS: Math problems
From: JohnInKansas
Date: 06 May 12 - 01:09 AM

The water & wine problem must conform to Murphy's axiom:

"You can't get anything clean without getting something else dirty,"

But also to the corollary:

"You can get everything dirty without getting anything clean."

(It's all in how far you spread the dirt.)

John

Subject: RE: BS: Math problems
From: MudGuard
Date: 06 May 12 - 03:41 AM

Wine and water:

if we assume there are no volume effects from mixing, then it is obvious that the amount of water in the wine must be exactly the same as the amount of wine in the water.

At the beginning we have two pints (or litres or liters or whatever) of liquid, exactly one half is water, exactly one half is wine.

At the end, we have two pints (or ...) of liquid. Still exactly one half is water and exactly the other half is wine.

As both containers contain exactly half of the liquid (one tablespoon of liquid was moved from A to B, and then one tablespoon was moved from B to A), whatever amount of water is missing from container A is now in container B. And, as we assumed no volume effects from mixing, exactly the same amount of wine is now in container A.

Unless someone has turned water into wine ...

Subject: RE: BS: Math problems
From: DMcG
Date: 06 May 12 - 05:02 AM

It's probably easier to see what is happening with the water and wine problem if you think about where each individual molecule is, rather than assuming the liquids are continuous. So to simplify it, do one of the sock experients; Imagine two boxes, one containing one hundred white socks and one containing 100 black socks. Take five from the 'black' box and put them in the white box. Then, eyes closed, mix them all about and without looking take five from the mixed box and put them back in 'black' box. Now, open your eyes! Are there more white socks in the black box or black socks in the white box? Obviously, they must be the same, since every sock is somewhere (unlike in real life!)and there are the same number of socks in each box as there was at the start.

Subject: RE: BS: Math problems
From: Mo the caller
Date: 06 May 12 - 05:59 PM

Isn't it time we met the hunter who went a mile due south, a mile due east, a mile due north and found himself back where he started. What colour was the bear that he shot?

Subject: RE: BS: Math problems
From: Louie Roy
Date: 06 May 12 - 10:49 PM

The bear was white this can only happen at the North Pole

Subject: RE: BS: Math problems
From: Jeri
Date: 06 May 12 - 11:46 PM

DMcG, that doesn't work so well because white/black socks will remain intrinsically white/black socks and wine will just get diluted. What if you grab a black sock and put it back into the black sock box? You'd have 96 black socks (and 4 white ones) in the black sock box and 95 white socks (5 black ones) in the white sock box.

We're talking about liquids, not solids. It's more like figuring out PPM (parts per million). It's about concentration or ratio, not numbers.

You removed a tablespoon of wine from the liter of wine.
You add the tablespoon of unadulterated wine to the water.

When you mix the tablespoon of wine into the liter of water, there will be SOME wine in it.

You removed a tablespoon of solution from the liter of what once was only water.
You add that tablespoon of water and a little wine to the wine.

There is less water in the wine than water in the water, because you added a tiny bit of wine back in. You didn't add any water back into the water.

Dick Greenhaus, come back here!

Subject: RE: BS: Math problems
From: MudGuard
Date: 07 May 12 - 02:16 AM

>> DMcG, that doesn't work so well because white/black socks will remain intrinsically white/black socks and wine will just get diluted. What if you grab a black sock and put it back into the black sock box? You'd have 96 black socks (and 4 white ones) in the black sock box and 95 white socks (5 black ones) in the white sock box.

96 black socks + 5 black socks = 101 black socks.
This would mean that one of the previous white socks has turned black.

What really happens:
after step one, in the white-sock-box you have 100 white socks and 5 black socks, and in the black-sock-box you have 95 black socks.

If you happen to pick 4 white + 1 black socks, after step 2 you have:
96 white socks + 4 black socks in the white-sock-box, and 96 black socks and 4 white socks in the black-sock-box.

Subject: RE: BS: Math problems
From: jonm
Date: 07 May 12 - 02:58 AM

The mile south/east/north and be back where you started has TWO possible locations.

The start point is the north pole. The bear is white.

The start point is approx. 1 and 1/6 miles from the south pole (so the mile east is an exact circle and the mile north retraces your initial steps. The bear is lost.

Subject: RE: BS: Math problems
From: Jeri
Date: 07 May 12 - 09:33 AM

I h8 math. :-)

Subject: RE: BS: Math problems
From: DMcG
Date: 07 May 12 - 01:09 PM

that doesn't work so well because white/black socks will remain intrinsically white/black socks and wine will just get diluted
Mudguard has it right, but as for dilution: as I said, think about it at a molecular level. What does it mean to say a single molecule of wine is diluted by one or more of water?   Now, if we are talking about the wine and water reacting chemically, that's a different matter. Take litre of H₂SO₄ and another litre of HCl and move a teaspoonful from one to the other ... that's quite a different experiment!

Subject: RE: BS: Math problems
From: DMcG
Date: 07 May 12 - 01:13 PM

Wrong choice of chemicals, but you get the idea! Pick an acid and an alkaline of your own preference.

Subject: RE: BS: Math problems
From: Bert
Date: 07 May 12 - 01:27 PM

The water wine problem is a logical problem as well as a mathematical one. If you have sets A and B which are of equal sizes and you take a subset of A and join it to set B. Then take a subset the same size as the previous one from set (B plus subset A) and return it to set A then the dilution of each set has got to be the same because the resulting sets are the same size.

Subject: RE: BS: Math problems
From: DMcG
Date: 07 May 12 - 02:16 PM

As for that bear, a lot depends on what the phrase 'a mile due north' means. If, for example it means 'face due north and walk a mile in a straight line' there are many more answers than the two given above.

Subject: RE: BS: Math problems
From: gnu
Date: 07 May 12 - 04:44 PM

DMcG... I can't think of any.

Subject: RE: BS: Math problems
From: DMcG
Date: 07 May 12 - 04:59 PM

Well, here's a different solution based on yet another interpretation of what 'go a mile north' could mean. Suppose it were to mean 'take one step in whatever direction is north; then another in whatever direction is north' and do that for say 2000 steps'. Now start one half-step from the north pole.

Subject: RE: BS: Math problems
From: DMcG
Date: 07 May 12 - 05:14 PM

(Of course, that's an engineer's definition of ending up in the same place, rather than a mathematicians. But however we handle to going east bit, the somewhat dizzy bear will never be more than one step away from where it started.)

Subject: RE: BS: Math problems
From: DMcG
Date: 07 May 12 - 05:45 PM

Ok, I've completely blown it. That only works for the north and east bit. Once you include the south part, you must end up a mile away.

Even so, I reckon moving north for a mile and east for a mile and staying in the bsame place is interesting in its own right!

Subject: RE: BS: Math problems
From: Mo the caller
Date: 08 May 12 - 08:12 AM

jonm. I like your lost bear solution.

Subject: RE: BS: Math problems
From: gnu
Date: 08 May 12 - 04:12 PM

This is, I believe, a "copycat" of The Fraside cartoon bt Garry Larrson (spg?).

http://www.threadless.com/submission/245734/One_of_these_penguins_IS_NOT_A_PENGUIN/showmore,designs

Subject: RE: BS: Math problems
From: gnu
Date: 08 May 12 - 04:13 PM

The Farside.

Subject: RE: BS: Math problems
From: Leadfingers
Date: 08 May 12 - 07:15 PM

Ten Squared

Subject: RE: BS: Math problems
From: gnu
Date: 08 May 12 - 08:01 PM

Hahahahaha... good one, Terry!