Tupler Die
Had a puzzle idea for yesterday. Didn't get it drawn and up because... I couldn't think of a name? Maybe it could go into the Hunt? I don't know, I just have excuses. Here's a different puzzle.
Backgammon has five dice: two for each player (though it can be played with a single pair of dice) and a "doubler die." The doubler die is used for scoring over multiple games, but what you need to know here is that the numbers on its faces are 2, 4, 8, 16, 32, and 64. So 2^1 through 2^6.
1. Take a large doubler die with its numbers written small enough for this task to make sense. Write some more digits so the faces display, in some order, the positive integers x, 2x, 3x, 4x, 5x, and 6x. Minimize x.
2. Take a large standard die with small writing instead of pips. So 1-6 are written on the faces. Add digits so the faces display the positive integers y, y^2, y^3, y^4, y^5, and y^6. Minimize y.
(Tricks optional.)
Backgammon has five dice: two for each player (though it can be played with a single pair of dice) and a "doubler die." The doubler die is used for scoring over multiple games, but what you need to know here is that the numbers on its faces are 2, 4, 8, 16, 32, and 64. So 2^1 through 2^6.
1. Take a large doubler die with its numbers written small enough for this task to make sense. Write some more digits so the faces display, in some order, the positive integers x, 2x, 3x, 4x, 5x, and 6x. Minimize x.
2. Take a large standard die with small writing instead of pips. So 1-6 are written on the faces. Add digits so the faces display the positive integers y, y^2, y^3, y^4, y^5, and y^6. Minimize y.
(Tricks optional.)