2017-05-08 Basic Practice Problems Online

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?

Problems of the Week

2017-05-08 Basic