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?

Upon reading this again, I came up with an even simpler solution than the one Nikki gave (which was the one I initally came up with)

Let x=10a+b. where a is any integer and b is an integer from -4 to 4. (If x=10a+5, x^2=100a^2+100a+25, which must have an even tens place.)  Then x^2=100a^2+20ab+b^2, but the only term that affects the tens place being odd/even is b^2, and only if it's greater than 10. So b^2 must be 16 which means the last digit must always be 6. This means the first brother writes a 2 dollar check to make up for half the difference between his extra 10 dollar bill, and the 6 one dollar bills.

Posted by Gamer on 2007-02-11 04:22:13