Math Is Fun Forum
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#1 2007-03-12 16:15:47
- JaneFairfax
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Janes 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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Re: Janes 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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Re: Janes puzzles
Brilliant! Youve nailed the answers down to a T! 
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#4 2007-03-13 08:46:48
- Zach
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Re: Janes 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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Re: Janes 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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Re: Janes puzzles
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#7 2007-03-14 02:03:29
- mathsyperson
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Re: Janes 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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Re: Janes 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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Re: Janes puzzles
Last edited by JaneFairfax (2007-03-14 09:26:50)
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#10 2007-03-14 05:37:46
- lightning
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Re: Janes 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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Re: Janes puzzles
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#12 2007-03-14 10:40:24
- mathsyperson
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Re: Janes 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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Re: Janes puzzles
Bingo! You got it at last. 
lightning dropped a great big hint with his wild guess, didnt he? 
My next puzzle will be a logic one
watch this space. 
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#14 2007-03-14 12:23:27
- Ricky
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Re: Janes 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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Re: Janes 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
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Re: Janes 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 girls instrument). From the clues below, can you work out which girl played which instrument, which composers 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? 
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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Re: Janes 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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Re: Janes puzzles
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#19 2007-03-14 17:06:38
- JaneFairfax
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Re: Janes puzzles
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#20 2007-03-14 17:56:06
- Ricky
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Re: Janes 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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Re: Janes puzzles
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#22 2007-03-14 19:06:51
- lightning
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Re: Janes 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
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Re: Janes puzzles
Sorry pi man, I missed your reply earlier.
Yes, youve got it. 
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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Re: Janes 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. 
Why did the vector cross the road?
It wanted to be normal.
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#25 2007-03-16 09:52:49
- JaneFairfax
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Re: Janes 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.
Anyway, Im out of puzzles for the moment you brainy people have solved the ones I have too quickly. Ill try and think of another puzzle or two now.
Last edited by JaneFairfax (2007-03-16 09:56:08)
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