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?

Since the first brother to draw also drew last, there is and odd number of $10 bills. Since they sell x sheep for $x dollars each, the amount of money they have is a perfect square.

The squares with an odd number in the tens place are 16 and 36. No square I've found after that would have an odd number of $10s. I'm not sure why that is.

Whether it is 16 or 36, there will be 6 $1 bills. To balance this, the brother must write a $2 check.

Posted by Tristan on 2003-10-06 13:49:56