Tale from Harvard Business Review

A Red Indian walks into a cafe with a shotgun in one hand and a bucketof buffalo manure in the other.
He says to the waiter, "Me want coffee."

The waiter says, "Sure chief, comin right up."

He gets the Indian a tall mug of coffee, and the Indian drinks it downin one gulp, picks up the bucket of manure, throws it intothe air,blasts it with the shotgun, then just walks out.

The next morning the Indian returns. He has his shotgun in one hand anda bucket of buffalo manure in the other. He walks up to thecounter andsays to the waiter, "Me want coffee."
The waiter says, "Whoa, Tonto! We're still cleaning up your mess fromyesterday. What the heck was all that about, anyway?"

The Indian smiles and proudly says, "Me training for uppermanagementposition:
Come in,
drink coffee,
shoot some crap,
leave mess forothers to clean up,
disappear for rest of day." : )))

Perfect Nos' Properties.....contd.

5. The even perfect numbers' final digits would go either 6 or 8.
6. Every even perfect no. is a triangular no.
7. Every even perfect no. can be written as sum of cubes of consecutive odd nos.

Some properties of perfect nos...

1. sum of reciprocals of all d divisors of a perfect no. is always 2.
2. Every even perfect no. can be written as 2^x-1(2^x-1), where 2^x-1 is a prime.
3. First 4 perfect nos. are 6, 28, 496 and 8128.
6=2^2-1(2²-1)
28=2^3-1(2³-1)
496=2^5-1(2⁵-1)
8128=2^7-1(2⁷-1)
4. Till d date, there is no known odd perfect no.It does not mean that thr is not any odd perfect no.

Perfect nos..

A perfect number is defined as a +ve integer which is the sum of its proper positive divisors, that is, the sum of the positive divisors excluding the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself)....

Happy New Year..

Since i ws nt wel..dts y cud nt be able 2 write any post...nw m back....well HAPPY NEW YEAR ...I WISH ALL OF U D EVERYTHING, THAT U SO WELL DESERVE...

digital root lesson....

The digital root (also repeated digital sum) of a number is the number obtained by adding all the digits, then adding the digits of that number, and keep on summing until a single-digit number is reached.
For example, the digital root of 73946 is 7, because 7 + 3 + 9 + 4 + 6 = 29 and 2 + 9 = 11 and 1 +1 =2....CONTD...

again a good question...

** How many +ve integral solutions of (x,y) exist for following equations:
(a) x^2-y^2 = 864
(b) x^2-y^2 = 945
(c) x^2-y^2 = 1616.

Road to success...

The Road to success is not straight...
There is a curve called failure...
A loop called confusionn...
Speed bumps called friends...
Red lights called enemies...
Caution lights called family...
You will have flats called jobs,

BUT...
If you have a spare called determination ...
An engine called perseverance ...
Insurance called faith...
A driver called God...
You will make it to a place called Success!

remainders.....

what is the remainder when 123123123.........upto 300 digits is divided by
a. 999
b.99

Divisibility......

For how many values of abc; 820abc is divisible by 7, 13 and 9????

Best of luck 4 ur exams..

In everything u do have a purpose, prepare to pursue ur purpose with a prayer, ask 4 guidance, protection and direction. Give thanks 2 answered prayers,have faith in your ability 2 succeed, be positive and never look back.If u keep all this in ur mind u wont wrong. Bst f luck 4 ur exams...