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?