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Wild tic-tac-toe is like traditional tic-tac-toe except that on each turn, a player may place an X or an O. The first person to get a row, column, or diagonal of three Xs or Os wins the game.
If Wild tic-tac-toe is played optimally, who should win?
This particular game ends on victory for player 2. The moves (and which player made them) are marked.
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1+1×2×3×41+2×3×4×51+3×4×5×6=52=112=192
Is 1 plus the product of four consecutive integers always a perfect square?
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This bowl is in the shape of the paraboloid z=x2+y2. A ball falls to the bottom such that it touches the lowest point (0,0,0) of the bowl.
What is the maximum possible radius of the ball?
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Two 1 kg beads are at the ends of a compressed spring resting on a smooth parabolic wire (y=x2). The spring has a natural length of 1 m and a force constant of 5 N/m.
If the system is in static equilibrium, how far away from the y-axis is each bead (in meters)?
Note: The spring is horizontal and gravity is 10 m/s2 in the −y direction.
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01234567891011121314…
The above is the beginning of all non-negative integers concatenated into a single infinite string.
111 is the first sub-string with 3 identical digits in a row, with different digits preceding and following the run of the identical digits. The first 1 of 111 comes at position 13 (from left) in the infinite string.
Where is the first such sub-string with 4 identical digits?
Give the position of the first digit of the four.
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