After reading the other threads, I decided that turns are bullshit and GJ's was much, much too easy for some members. So, I'm going to post up a few my precalc teacher gave out. I've solved all of these and may give basic hints if no one gets them. PM me the answer, and after twelve hours I will post the correct answer. Don't ruin the slow people's fun =]
There are a three total, here is number one.
On a remote island all of the natives belong to one of two tribes: the Brights, who are so brilliant at numerical calculations that they always get the correct answer, and the Braves, who bravely rush in to do calculations beyond their ability and never get the right answer. (The Braves are not entirely stupid: they can do simple counting and comparing of numbers, but they always get arithmetic calculations wrong.) Both Brights and Braves pride themselves on their complete honesty. They always tell the truth, or (in the case of Braves) at least what they believe to be the truth; they never purposely tell a lie (unlike the folks on some of those other islands).
One day a group of natives was playing a game of Numberskulls. There were 5 players and a moderator. The moderator, who was a Bright, painted a 3-digit number on each of the players' foreheads, so that each could see all numbers but their own. All 5 of the numbers were different. The moderator would ask them questions in turn about the numbers they could see, and from the answers they would try to deduce what number was on their own forehead. The first to do so was the winner. What follows is a record of the game, with questions omitted and players designated by letters.
(1) A: I see exactly 1 prime number.
(2) B: I see exactly 2 prime numbers.
(3) C: I see exactly 3 perfect squares.
(4) D: I see exactly 3 triangular numbers.
(5) E: I see exactly 3 perfect squares.
(6) A: I see exactly 3 numbers with a digital sum of 10.
(7) B: I see exactly 3 numbers whose square root is more than 25.
(8) C: I see exactly 0 numbers with a digital sum of 10.
(9) D: I see exactly 3 perfect cubes.
(10) E: I see exactly 0 numbers with a digital product of 18.
At this point one of the players announced his number and won. (Of course it was a Bright; for some reason Braves never win these games, a point of much amusement to the Brights!)
What number was on each player's forehead?
There are a three total, here is number one.
On a remote island all of the natives belong to one of two tribes: the Brights, who are so brilliant at numerical calculations that they always get the correct answer, and the Braves, who bravely rush in to do calculations beyond their ability and never get the right answer. (The Braves are not entirely stupid: they can do simple counting and comparing of numbers, but they always get arithmetic calculations wrong.) Both Brights and Braves pride themselves on their complete honesty. They always tell the truth, or (in the case of Braves) at least what they believe to be the truth; they never purposely tell a lie (unlike the folks on some of those other islands).
One day a group of natives was playing a game of Numberskulls. There were 5 players and a moderator. The moderator, who was a Bright, painted a 3-digit number on each of the players' foreheads, so that each could see all numbers but their own. All 5 of the numbers were different. The moderator would ask them questions in turn about the numbers they could see, and from the answers they would try to deduce what number was on their own forehead. The first to do so was the winner. What follows is a record of the game, with questions omitted and players designated by letters.
(1) A: I see exactly 1 prime number.
(2) B: I see exactly 2 prime numbers.
(3) C: I see exactly 3 perfect squares.
(4) D: I see exactly 3 triangular numbers.
(5) E: I see exactly 3 perfect squares.
(6) A: I see exactly 3 numbers with a digital sum of 10.
(7) B: I see exactly 3 numbers whose square root is more than 25.
(8) C: I see exactly 0 numbers with a digital sum of 10.
(9) D: I see exactly 3 perfect cubes.
(10) E: I see exactly 0 numbers with a digital product of 18.
At this point one of the players announced his number and won. (Of course it was a Bright; for some reason Braves never win these games, a point of much amusement to the Brights!)
What number was on each player's forehead?
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