# Problems of the Week

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# 2017-06-26 Basic

A square and a circle have the same perimeter.

Which has a larger area, the square or the circle?

Two people are playing rock-paper-scissors. They both have the same strategy:

• If win, play the same move again the next round.
• Otherwise, play the move that defeats the opponent's last move.

In the first round, the match-up is rock versus paper. If they continue playing round after round, will a round ever end in a draw?

I have a 100 ml mixture that is 20% isopropyl alcohol (80 ml of water and 20 ml of isopropyl alcohol).

How much more alcohol do I need to add to make the mixture 25% alcohol?

On an island, there are only 2 types of people: knights who only tell the truth and knaves who always lie.

Interestingly, no islander can ever make the statement "I am a knave."

However, can a married islander make this statement?

"My wife and I are both knaves."

Note that this is considered a single statement that is either true (as a whole statement) or false (as a whole statement).

A cyclist is riding a bicycle of wheel radius $r$ along the edge of a rotating disk of radius $R\, (>r)$ in such a way that he appears to be stationary to a person standing on the ground.

If the tires of the bicycle don't slip on the disk (that is, the contact points of the wheel and the disk have equal velocities), then which will have a greater rotating speed?

Clarification: The "rotating speed" is the angular speed (or the magnitude of the angular velocity) given by the rate of change of $\theta$ with respect to the axis about which it is rotating:

$\omega = \dfrac{d\theta}{dt}$

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