Brain Teasers
The Brother's Check
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 a few $1 bills (less than 10 of them). 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 for?
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Hope you don't mind my rewrite of your answer. Your version just seemed a little confusing.
Not at all Bobbrt. You are the more experienced guy and hence you should be knowing how to make the riddles more simpler than me.
The answer should read "Any *square* number
with an odd number in the 10's place..."
The reason is that you can write x as
10*a+b, where a and b are integers with b
between 0 and 9. The square of this number is
100*a^2 + 20*a*b + b^2. This number will
have an odd digit in the tens place if and only
if b^2 does - which means b must be 4 or 6 (checking
the squares of numbers from 0 to 9).
with an odd number in the 10's place..."
The reason is that you can write x as
10*a+b, where a and b are integers with b
between 0 and 9. The square of this number is
100*a^2 + 20*a*b + b^2. This number will
have an odd digit in the tens place if and only
if b^2 does - which means b must be 4 or 6 (checking
the squares of numbers from 0 to 9).
As soon as I realised there had to be an odd number of $10 bills I thought of 6^2 = 36 which fitted the description in the teaser. The answer was $4 for this number and I guessed either the result would be the same for other numbers that fitted or the teaser had multiple answers which not have been very satisfactory so I went with $4.
OK teaser.
OK teaser.
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