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krassi_holmz
2005-12-05 17:09:52

Ganesh,
I think c) proof isn't very right. Because you have "let" here. Here's a proof without "let":
(b means black, w means white)
Let...
b1+w1=b2
b2+w2=b3
so
b1+w1+w2=b3; b1+(w1+w2)=b3,
but
b1+w3=b3, so w1+w2=w3.

Ricky
2005-12-05 08:17:00

Draw the triangle, and then draw it again rotated so that B is in the same corner that C was.  Now since ICA < IBA and ICB < IBC, ICA + ICB < IBA + IBC.  Since this is true, the angle at C is less than the angle at B.  I forget the name of the proof, but if you have such a triangle, the side with a greater angle has a smaller diagonal (BB' and CC').  So Since angle C < B, CC' > BB'.

I don't understand quite understand the wording in 2.

math
2005-10-31 19:48:52

the problem were unsolve in along time ago !!!!!!!!!

math
2005-10-30 18:27:00

math
2005-10-27 08:41:27

next week , i will give the proof to my teacher ,please , !!!!!!!

math
2005-10-25 21:40:33

very thanks to ganesh !!!!

ganesh
2005-10-25 14:13:22

#### math wrote:

C)in assemble N ,every number is white or black so that white + black=black
prove : white + white = white

Let white=0, black=1;
white + black = 0 + 1 = 1 = black
white + white = 0 + 0 = 0 = white, Proved!

For A), B) please give some time. Yes, Proofs aren't too easy. They are time consuming.

math
2005-10-24 22:09:08

MathsIsFun
2005-10-24 07:39:56

Maybe ganesh could post these one at a time under "Ganesh's Puzzles".

Flowers4Carlos
2005-10-24 07:10:12

never fear!!!  Flowers4Carlos is here to save the day!!!!

*looks at the problem*

eeeeek..... *falls down*

math
2005-10-24 02:32:50

nobody

math
2005-10-20 21:56:06

thanks . I will be waiting for you

MathsIsFun
2005-10-20 16:09:16

Yes, that's right ... I said it wasn't really a proof.

I am sorry, but your questions are difficult, I am just hoping someone can spare the time to work on answer for you. I have unfortunately been a little busy recently.

math
2005-10-20 13:09:34

MathsIsFun
2005-10-18 23:11:01

No, not yet. Proofs are very difficult.

Ideas are easy, though. For "C" I can think of:

white + black=black
therefore: black-black=white, but black-black=0
therefore: white+white = 0 + 0 = 0 = white

But this is not really a proof