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Monthly Archives for November, 2014

Space filling curve

Posted on: November 29th, 2014 by

Can you find a continuous function from the unit interval [0,1] to the unit square [0,1]^2? In other words, can you find a curve that passes through all points in a unit square?

Coin covering puzzle

Posted on: November 27th, 2014 by

100 identical circular coins are placed in a rectangular table such that no extra coin can be placed without overlapping with one of the coins already on the table. For the purpose of this puzzle, assume a coin is placed on a table as long as it's center lies on the table. Show that with 400 coins, one can cover the entire surface area of Continue reading the story "Coin covering puzzle"

Parabola puzzle

Posted on: November 25th, 2014 by
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Let y=ax^2+b_1x+c_1 and y=ax^2+b_2x+c_2 be two parabolas with the same coefficient for the x^2 term. The y-intercepts of the two parabolas are (0,c_1) and (0,c_2) respectively. Let the two parabolas intersect at (x_1,y_1) and let the tangent to the two parabolas drawn at (0,c_1) and (0,c_2) intersect at (x_2,y_2). Show using physics that x_1=x_2. Hint: Assume x is time and y is space, and there is Continue reading the story "Parabola puzzle"

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