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#101 2005-08-22 23:07:47

justlookingforthemoment
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Registered: 2005-05-26
Posts: 2,161

Re: Problems and Solutions

And 'Ganesh's Puzzles' doesn't have a subtitle anymore.

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#102 2005-08-22 23:49:49

MathsIsFun
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Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

LOL, mathsy! I put the "z" there when I was trying to get them to work ... to tell you the truth, in all the confusion, I kinda' lost count, and given that this is a 44 magnum, the most powerful handgun in the world, ... sorry, where was I?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#103 2005-08-23 21:04:41

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem #k+1
In a University, a student has to take necessarily Physics, Chemistry or Mathematics. The students are permitted take any two of them or even all the three of them. If 85 students take Physics, 65 students take Chemistry, 100 students take mathematics, 30 students take both Physics and Chemistry, 40 students take both Physics and Mathematics and none of the students take Chemistry and Mathematics or all three of them, how many students are there in the University?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#104 2005-08-23 22:56:28

wcy
Member
Registered: 2005-08-04
Posts: 117

Re: Problems and Solutions

this could be done by drawing a Venn diagram, i suppose

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#105 2005-08-24 16:34:02

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem #k+2

I have a certain number of eggs in my store.
If you divide the number of eggs by 2 there will be one egg left.
If you divide the number of eggs by 3 there will be two eggs left.
If you divide the number of eggs by 4 there will be three eggs left.
If you divide the number of eggs by 5 there will be four eggs left.
If you divide the number of eggs by 6 there will be five eggs left.
If you divide the number of eggs by 7 there will be six eggs left.
If you divide the number of eggs by 8 there will be seven eggs left.
If you divide the number of eggs by 9 there will be eight eggs left.
If you divide the number of eggs by 10 there will be nine eggs left.

If you divide the Number of eggs by 11 there will be NO EGGS left!
What is the minimum number of eggs I can have in my store?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#106 2005-08-25 20:26:53

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem #k+3

A cube of dimensions 10cm x 10cm x 10cm is made up of smaller cubes of dimensions 1cm x 1cm x 1cm. If the outermost layer of smaller cubes are taken off, how many smaller cubes would be left?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#107 2005-08-26 18:39:59

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem #k+4

A polyhedron has 12 faces(sides) and 18 edges. How many vertices does it have?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#108 2005-08-27 11:34:15

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

It does look odd - that is my "hide" tag misbehaving. Job for me, hey?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#109 2005-08-27 22:10:23

wcy
Member
Registered: 2005-08-04
Posts: 117

Re: Problems and Solutions

what happened to the old problems before the forum got hacked?

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#110 2005-08-28 06:54:39

Roraborealis
Member
Registered: 2005-03-17
Posts: 1,594

Re: Problems and Solutions

The ones in the Puzzles and Games board?


School is practice for the future. Practice makes perfect. But - nobody's perfect, so why practice?

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#111 2005-08-29 20:03:52

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Solution to problem#k+3 : kylekatarn is correct.

Problem # k+5

Use each digit 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 exactly once to form two five-digit numbers that when multiplied produce the largest quantity.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#112 2005-08-29 20:54:45

MathsIsFun
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Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

You mean like this:  97531×86420 = 8428629020  ?

Can anyone do better?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#113 2005-08-29 23:28:17

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Thats what I thought of immediately on seeing the problem!
I am not saying you're correct, I'm not saying you're wrong....
I leave the problem open for some days smile


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#114 2005-08-30 18:01:22

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem # k+6

A woman and her grandson have the same birthday. For six consecutive birthdays, she is an integral multiple of his age. How old is the grandmother at the sixth of these birthdays?

(This was true for me and my maternal grandmother, although we didn't have the same birthday. For most of 6 consecutive years, her age was an integral multiple of mine) smile


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#115 2005-08-30 20:06:41

Jai Ganesh
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Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem # k+7

Mike and Jim attempted to solve a quadratic equation. Mike
made a mistake in writing down the constant term. He ended up with the
roots (4, 3). Jim made a mistake in writing down the coefficient of x. He
got the roots as (3, 2). What are the roots of the original quadratic equation?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#116 2005-08-31 09:44:09

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

I know I have to sit down and make that [hide]tage work properly ... maybe I will get a chance in the next few days.

Nice work on the solution kylekatarn, that was some silly mistake they made! (BTW b'=-5 I think)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#117 2005-08-31 10:47:03

MathsIsFun
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Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

Didn't affect the result, I only noticed it because I was trying to understand how you solved it!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#118 2005-08-31 16:19:31

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

The solution to problem # k + 7 given by kylekatarn is correct.
The sum of the roots is 7 and their product is 6.

Problem # k+8

In a number system the product of 44 and 11 is 2124. The
number 3111 of this system, when converted to the decimal number system, becomes____________.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#119 2005-08-31 19:39:11

wcy
Member
Registered: 2005-08-04
Posts: 117

Re: Problems and Solutions

my answer is

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#120 2005-08-31 20:43:02

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

You are correct, wcy.
Good, you didn't tell how you did it smile
Try earlier problems too.


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#121 2005-08-31 21:00:03

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Problem # k + 9

A square, whose side is 2 meters, has its corners cut away so as
to form an octagon with all sides equal. Then, what is the length of each side of the octagon, in meters?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#122 2005-08-31 21:21:29

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

Ganesh, I am thinking of an upgrade to the "hide" tag.

Wouldn't it be cool if we could really hide the results from everyone (except moderators) until a certain time, maybe 1 week after the post, or based on the time you post the question.

A third possibility would be for you to have a keyword in the topic like "open" and that could be what controls whether the hide tag really hides, so "Ganesh's Puzzles" would be a list of solved/unsolved puzzles, with other peoples answers hidden until you let them be shown.

I would obviously need to program all this, and I am not sure the hurdles I would face, but what do you think of the idea?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#123 2005-08-31 22:10:01

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

The idea seems great!
Inspite of the hide tag, its too tempting for many to view the answer.
Since most of our members solve the problems and post their solutions in a day or two, I post a problem or two everyday. Once the problem is solved, I forget to tell how it is done.
Your idea would be of great help smile


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#124 2005-09-01 00:29:43

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,711

Re: Problems and Solutions

So, do you think it would be good to post a new topic for every puzzle? That way they could have titles like "Cut a Square (Current)", which you can edit to "Cut a Square" when it is solved. I could use the phrase "(Current)" to tell the forum to really hide answers in the hide tag.

Also, if someone posts a full answer you can edit their post, insert a "hide" tag and put a gentle reminder to use the hide tag smile

(This is all based on the assumption I can get the hide tag to work like we want!)


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#125 2005-09-01 16:59:11

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,957

Re: Problems and Solutions

Yes, that seems a good suggestion.

Two tricky problems to start the day:-

Problem # k + 10
Complete the series:-
1248, 1632, 6412, 8256, _____


Problem # k + 11
What is special about the number 2592?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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