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#1 2007-03-12 16:15:47

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Jane’s puzzles

1. Without using any program (computer or otherwise), how quickly can you find the prime factors of the following numbers?
(i) 359 999
(ii) 1 209 991

(Note: You may use a calculator to help you with your arithmetical calculation, but only a simple, pocket calculator. Use any sort of program is not allowed.)

2. Nine drinking cups are placed in a row. They are alternately right-way up and upside down, the two cups at the ends being upside down. The game consists of turning the cups over two at a time, until all the cups are right-way up. But the question is:

Can this be achieved? If not, why not?

3. Explain how it can be true that 11 + 1 = 111.

Last edited by JaneFairfax (2007-03-12 16:21:32)

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#2 2007-03-12 23:00:26

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Jane’s puzzles


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-03-13 03:36:58

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

Brilliant! You’ve nailed the answers down to a T! ThumbsUp.gif

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#4 2007-03-13 08:46:48

Zach
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Registered: 2005-03-23
Posts: 2,075

Re: Jane’s puzzles


Most obviously the wrong answer.


Boy let me tell you what:
I bet you didn't know it, but I'm a fiddle player too.
And if you'd care to take a dare, I'll make a bet with you.

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#5 2007-03-13 11:59:14

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Jane’s puzzles


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#6 2007-03-13 13:42:06

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

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#7 2007-03-14 02:03:29

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Jane’s puzzles


Why did the vector cross the road?
It wanted to be normal.

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#8 2007-03-14 02:21:36

lightning
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Registered: 2007-02-26
Posts: 2,060

Re: Jane’s puzzles


Zappzter - New IM app! Unsure of which room to join? "ZNU" is made to help new users. c:

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#9 2007-03-14 05:24:37

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

Last edited by JaneFairfax (2007-03-14 09:26:50)

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#10 2007-03-14 05:37:46

lightning
Real Member
Registered: 2007-02-26
Posts: 2,060

Re: Jane’s puzzles


Zappzter - New IM app! Unsure of which room to join? "ZNU" is made to help new users. c:

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#11 2007-03-14 09:26:29

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

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#12 2007-03-14 10:40:24

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Jane’s puzzles


Why did the vector cross the road?
It wanted to be normal.

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#13 2007-03-14 12:04:26

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

Bingo! You got it at last. big_smile

lightning dropped a great big hint with his wild guess, didn’t he? rolleyes

My next puzzle will be a logic one … watch this space. wink

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#14 2007-03-14 12:23:27

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Jane’s puzzles


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#15 2007-03-14 12:31:39

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Jane’s puzzles


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#16 2007-03-14 12:39:38

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

#4. Five girls of different ages entered a music competition, playing pieces by different composers on different instruments (each piece being arranged for each girl’s instrument). From the clues below, can you work out which girl played which instrument, which composer’s piece was arranged for which which girl to play, how old each girl was and what position each girl achieved in the competition, and then answer the question below?

(1) The average age of the five girls was 17. The youngest girl was 13 while the 20-year-old Emma was the oldest.

(2) Amelia, who came first, was older than the girl who played the clarinet, but younger than the girl who played a piece by Schubert, who was not placed third or fifth.

(3) Harriet was not the girl who played a piece by Brahms on the piano, who finished above Isabella but did not win the competition.

(4) Becky chose to play something by Haydn, but she was not the 15-year-old girl who performed on the cello; the latter did not play a piece by Beethoven.

(5) The girl who displayed her talents with a piece by Mozart achieved fourth place, but the violin was not the instrument on which the 18-year-old girl showed off her musical ability.

The question is: Who played the flute? roll

Last edited by JaneFairfax (2007-03-14 20:13:51)

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#17 2007-03-14 14:06:20

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Jane’s puzzles


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#18 2007-03-14 17:06:16

pi man
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Registered: 2006-07-06
Posts: 251

Re: Jane’s puzzles

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#19 2007-03-14 17:06:38

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

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#20 2007-03-14 17:56:06

Ricky
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Registered: 2005-12-04
Posts: 3,791

Re: Jane’s puzzles


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#21 2007-03-14 18:00:40

JaneFairfax
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Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

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#22 2007-03-14 19:06:51

lightning
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Registered: 2007-02-26
Posts: 2,060

Re: Jane’s puzzles

whats next


Zappzter - New IM app! Unsure of which room to join? "ZNU" is made to help new users. c:

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#23 2007-03-14 20:12:55

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

pi man wrote:

Sorry pi man, I missed your reply earlier.

Yes, you’ve got it. up

Last edited by JaneFairfax (2007-03-14 20:14:57)

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#24 2007-03-15 00:22:40

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Jane’s puzzles

Technically, we don't know if anyone plays the flute, because none of the hints say that anyone does, or even mention a flute.

But then again, you could use similar reasoning to tear the whole puzzle apart. Just because the 18-year old didn't use the violin doesn't mean that someone else did, etc. So it's probably safer to just assume that pi man's right. tongue


Why did the vector cross the road?
It wanted to be normal.

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#25 2007-03-16 09:52:49

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: Jane’s puzzles

The puzzle follows the conventional format for such logic puzzles: you are given several sets of n elements each, and the aim is to find the correct bijections between the sets. So if you have matched (n−1) members between two sets, the last remaining member of one set must automatically match that of the other set. wink

Anyway, I’m out of puzzles for the moment – you brainy people have solved the ones I have too quickly. tongue I’ll try and think of another puzzle or two now.

Last edited by JaneFairfax (2007-03-16 09:56:08)

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