Problems of the Week

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2018-09-10 Basic

         

When coloring a map, each region must be filled with a single, solid color and no two regions with touching edges can be the same color.

Given that these two regions have already been colored red, what is the minimum number of colors needed (including the red already used) to color the entire map?

You hear 3 snaps when someone breaks up a \(2 \times 2\) chocolate bar into \(1 \times 1\) pieces, 8 snaps when it's a \(3 \times 3\) bar, and 15 snaps when it's a \(4 \times 4\) bar.

How many snaps will you hear when an \(8 \times 8\) chocolate bar is split into \(1 \times 1\) pieces?

Details and Assumptions:

  • You cannot break two or more pieces at once.
  • Breaks must be made either horizontally or vertically.

A large spherical planet is made entirely of an incompressible liquid. What is the pressure at the center of this planet?

All four Kings from a deck of cards are placed face down on a table in a random order. You select two of them, and if both are the same color (red or black), then you win.

What’s your chance of winning?

A car accelerates from rest to 50 km/hr and then from 50 km/hr to 100 km/hr. Assume there is no air drag.

In which case does the engine of the car do more work?

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