Two brothers share a flock of x sheep. They take the sheep to the market and sell each sheep for $x. At the end of the day they put the money from the sales on the table to divide it equally. All money is in $10 bills, except for fewer than ten excess $1 bills. One at a time they take out $10 bills. The brother who draws first also draws last.

The second brother complains about getting one less $10 bill so the first brother offers him all the $1 bills. The second brother still received a total less than the first brother so he asks the first brother to write him a check to balance the things out.

How much was the check?

check was of Rs. 2.

let us consider x to be any number

x=10y+z ----- (1)

sqauring eqn. (1)

x^2=100y^2+z^2+20yz ------------- (2)

eqn. (2) represents the total amount after selling all the sheeps.

now,

eqn(2) % 10 = no. of one rupee note
eqn(2) / 10 = no. of ten rupee note

now,

eqn(2) % 10 = z^2 % 10 -------(3)
/* others terms being divisible by 10 */

eqn(2) / 10 = 10y^2 + 2yz + (z^2)/10

since we can observe that total no. of 10 rupee note will be a odd number-

we conclude,

(z^2)/10 is a odd number.--------(4)

possible value of z = 1,2,3,4,5,6,7,8,9

eqn (4) is true only for z=4,6.

eqn (3) gives 6 as result for z=4 and 6

hence, 6 one rupee notes are there..

so Rs. 2 transfer from Big B to choota bhai will divide the money equally..
AND THEY CAN LIVE HAPPILY THERE AFTER ..........

Posted by Sandeep on 2003-11-03 11:33:44