Problems and Solutions

Jai Ganesh · 2005-09-14 16:20:31

John E. Franklin · 2005-09-14 17:00:33

Jai Ganesh · 2005-09-14 18:07:57

Your are correct, John!

well%20done%20lge.gif

John E. Franklin · 2005-09-15 11:01:51

Last edited by John E. Franklin (2005-09-15 11:04:36)

Jai Ganesh · 2005-09-15 17:09:20

maurlady · 2005-09-18 13:03:18

= 252001 ???

ganesh wrote:

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 · 2005-09-18 16:10:43

kylekatarn wrote:

solved problem #k+20 (finnaly, I think)

And solved it correctly! Well done, Kylekatarn!!!

And the solution to problem # k + 2 is a much smaller number!
It is

Jai Ganesh · 2005-09-19 16:07:22

Problem # k + 23

A Pythagorean triple is a set of three numbers (a,b,c) such that
a² + b² = c². For example, (3,4,5).
Prove that three prime numbers cannot form a Pthagorean triple.

mathsyperson · 2005-09-28 05:24:25

The current unsolved problems are k+(1, 4, 15, 16, 19, 22, 23), but I think I've seen k+23 somewhere before.

mathsyperson · 2005-09-28 05:37:41

I was wrong, I'd seen this before, and it's similar.

Anyway, here's my answer to k+23:

It's kind of sloppy. And here's

, too.

mathsyperson · 2005-09-28 06:33:44

k+1 needs a Venn diagram (I think) and I don't have knowledge of them (yet ) so I'll leave it.

k+19 seems do-able, but it needs more thought than the others, so I'll leave it for now.

Last edited by mathsyperson (2005-09-28 06:41:58)

Jai Ganesh · 2005-09-30 18:27:51

Mathsy, all your solutions are correct! You had understood problem # k + 16 rightly!

wcy · 2005-10-05 01:04:21

Problem # k + 23

A Pythagorean triple is a set of three numbers (a,b,c) such that
a² + b² = c². For example, (3,4,5).
Prove that three prime numbers cannot form a Pthagorean triple.

Case 1:
Prime numbers are all odd except 2, so a² is odd, b² is odd, and c² is also odd. But, a²+b² is even if both of them are odd. Contradiction!!

Case 2:
a=2
4+b²=c²
c²-b²=4
(c-b)(c+b)=4
the only possibilities are (c-b)=1, (c+b)=4
2c=5
c=2.5 (rejected)

Case 3:
a=b=2
4+4=c²
c²=8^0.5 (rejected)

Case 4:
a=b=c=2 (rejected immediately :P)

Last edited by wcy (2005-10-05 01:05:04)

MathsIsFun · 2005-10-05 11:04:21

wcy wrote:

Prime numbers are all odd except 2, so a² is odd, b² is odd, and c² is also odd. But, a²+b² is even if both of them are odd. Contradiction!!

Very neatly put.

Jai Ganesh · 2005-10-06 16:03:32

Problem # k + 24

A cube is made by cutting off the excess portions of a sphere of radius r. What is the volume of the biggest cube that can be formed?

mathsyperson · 2005-10-06 19:05:27

I think it's...

Last edited by mathsyperson (2005-10-06 19:08:21)

Jai Ganesh · 2005-10-06 21:40:24

You are right, Mathsy!

wcy · 2005-10-07 00:19:12

wow that was a rather tough one to understand

Jai Ganesh · 2005-10-07 23:19:39

Problem # k + 25

Three mathematics classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.

What is the average of all the three classes?

mathsyperson · 2005-10-08 00:09:21

I'm not entirely sure, but

Last edited by mathsyperson (2005-10-08 00:17:50)

Jai Ganesh · 2005-10-09 16:38:49

You are right Mathsy. The solution to the problem given was 81.5, which is certainly incorrect! I would solve the problem exactly the way you did
(I thought of the method of solving at the time of posting, but didn't actually solve it!)

Jai Ganesh · 2005-10-09 16:48:15

Problem # k + 26

There are 2 brothers among a group of 10 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

mathsyperson · 2005-10-09 17:57:19

Jai Ganesh · 2005-10-09 18:09:38

Jai Ganesh · 2005-10-10 00:33:15

Problem # k + 27

What is the value of (1-Cos2A) / (1+Cos2A) given that tan A = 3/4 ?

Math Is Fun Forum

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