Problems and Solutions

justlookingforthemoment · 2005-08-22 23:07:47

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

MathsIsFun · 2005-08-22 23:49:49

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?

Jai Ganesh · 2005-08-23 21:04:41

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?

wcy · 2005-08-23 22:56:28

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

Jai Ganesh · 2005-08-24 16:34:02

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?

Jai Ganesh · 2005-08-25 20:26:53

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?

Jai Ganesh · 2005-08-26 18:39:59

Problem #k+4

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

MathsIsFun · 2005-08-27 11:34:15

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

wcy · 2005-08-27 22:10:23

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

Roraborealis · 2005-08-28 06:54:39

The ones in the Puzzles and Games board?

Jai Ganesh · 2005-08-29 20:03:52

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.

MathsIsFun · 2005-08-29 20:54:45

You mean like this: 97531×86420 = 8428629020 ?

Can anyone do better?

Jai Ganesh · 2005-08-29 23:28:17

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

Jai Ganesh · 2005-08-30 18:01:22

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)

Jai Ganesh · 2005-08-30 20:06:41

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?

MathsIsFun · 2005-08-31 09:44:09

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)

MathsIsFun · 2005-08-31 10:47:03

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

Jai Ganesh · 2005-08-31 16:19:31

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____________.

wcy · 2005-08-31 19:39:11

my answer is

Jai Ganesh · 2005-08-31 20:43:02

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

Jai Ganesh · 2005-08-31 21:00:03

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?

MathsIsFun · 2005-08-31 21:21:29

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?

Jai Ganesh · 2005-08-31 22:10:01

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

MathsIsFun · 2005-09-01 00:29:43

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

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

Jai Ganesh · 2005-09-01 16:59:11

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?

Math Is Fun Forum

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