Here are two brainteasers for those bored at work this Tuesday.
If you know the answer to the easier one right away, attempt a solution at the harder one as well before posting
your solution to allow others a chance to solve it as well.
Problem #1 "Brazilian Football" (Easy):
In standard American Football, 7 points are awarded for a touchdown (if the extra-point kick is succesful), and 3 points are awarded for a field goal. Assuming these are the only way ways to score (and every extra-point kick
after a touchdown is succesful), then the highest impossible team score in US Football is 11 points-- any higher score can be attained through some combination of touchdowns and field goals.
Let's say they start playing American Football in Brazil, but every year they adjust the number of points awarded for each score to compensate for inflation. After 5 years, a touchdown in "Brazilian Football" is worth 43 points (if the extra kick is succesful) and a field goal is worth 17 points. Is there a highest impossible team score if these are the only two scoring methods, and if so, what is it?
Problem #2 "Making Money in a Down Market" (Harder):
Let's say that you have a choice between two mutual funds to invest a fixed amount of money into.
Fund A is very predictable, but in a bad way: every fifth day, it's value drops 1%. The other days the value remains completely unchanged.
Fund B is wild, but flat: Each day, there is a 50% chance the value goes up 10%, and a 50% chance the value goes down 10%
Is there some investment strategy you can follow that will guarantee you a long-term profit? If so, what is it? Or if not, why not? You must keep all of your money in the two investments, so your choice each day is how much of your money to invest in each Mutual Fund.
Does anything change if Fund B instead has a 50% chance to double in value, and a 50% to halve in value each day?
If you know the answer to the easier one right away, attempt a solution at the harder one as well before posting
your solution to allow others a chance to solve it as well.
Problem #1 "Brazilian Football" (Easy):
In standard American Football, 7 points are awarded for a touchdown (if the extra-point kick is succesful), and 3 points are awarded for a field goal. Assuming these are the only way ways to score (and every extra-point kick
after a touchdown is succesful), then the highest impossible team score in US Football is 11 points-- any higher score can be attained through some combination of touchdowns and field goals.
Let's say they start playing American Football in Brazil, but every year they adjust the number of points awarded for each score to compensate for inflation. After 5 years, a touchdown in "Brazilian Football" is worth 43 points (if the extra kick is succesful) and a field goal is worth 17 points. Is there a highest impossible team score if these are the only two scoring methods, and if so, what is it?
Problem #2 "Making Money in a Down Market" (Harder):
Let's say that you have a choice between two mutual funds to invest a fixed amount of money into.
Fund A is very predictable, but in a bad way: every fifth day, it's value drops 1%. The other days the value remains completely unchanged.
Fund B is wild, but flat: Each day, there is a 50% chance the value goes up 10%, and a 50% chance the value goes down 10%
Is there some investment strategy you can follow that will guarantee you a long-term profit? If so, what is it? Or if not, why not? You must keep all of your money in the two investments, so your choice each day is how much of your money to invest in each Mutual Fund.
Does anything change if Fund B instead has a 50% chance to double in value, and a 50% to halve in value each day?
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