# Problems of the Week

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# 2017-05-08 Basic

Bill, David, and Joey are the 3 finalists in a hot dog eating contest.

• Bill did not eat the fewest hot dogs.
• David did not eat the greatest number of hot dogs.
• Joey ate more hot dogs than Bill.

Who won the contest by eating the most hot dogs?

True or False?

If real numbers ${\color{#D61F06}a},\ {\color{#3D99F6}b},\ x,$ and $y$ satisfy ${\color{#D61F06}a}x + {\color{#3D99F6}5}y = {\color{#D61F06}2}x + {\color{#3D99F6}b}y,$ then it must be the case that ${\color{#D61F06}a=2} \text{ and } {\color{#3D99F6}b=5}.$

A baseball bat is not uniformly shaped, which is why its center of mass is not at the midpoint between its two ends.

Suppose we cut a baseball bat (perpendicular to its axis) into two pieces through its center of mass, as shown above. Which piece will have greater mass?

Hint: if you're not familiar with the idea of the center of mass, it is the position about which we could balance the bat if we placed it on a knife's edge.

Can the $\pi$ figure above, composed of 5 pieces of different colors, be rearranged into a perfect square?

The individual pieces can be rotated, reflected and translated.

Each of the nodes--the small circles--of the squares below may or may not have a bomb. The number in each square indicates the number of bombs planted around that square.

How many nodes have bombs?

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