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?

(In reply to Solution by nikki)

nikki, beautiful! i got the solution too but by inspection, and was stumped as to why all my units place numbers were 6 for (x*x) with an odd tens place number...but you just proved it. and a smart way to prove it too!
-mohan.

Posted by mohan on 2003-10-07 04:42:17