# Problems of the Week

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# 2017-09-18 Basic

A train that is 10 km in length traveling at 10 km/hour is about to enter a tunnel that is 10 km long.

How long will it take for the entire train to get through the tunnel, from when the front of the train enters the tunnel to when the end of the train exits the tunnel?

A water tanker is rolling on a horizontal, frictionless surface and continuously leaks water from a hole in the bottom.

Over time, the mass of the tanker decreases and its speed $\text{\_\_\_\_\_\_\_\_\_\_}.$


Assume that the water drips such that it doesn't affect the tires.

$X,$ $X+2,$ and $X+4$ are all prime numbers when $X=3.$ Is this true for any other $X?$

There is an old telescope. As shown in the figure, the lower half of its lens is covered by dust so that no light can pass through, while the upper half is still clean. If we use this telescope to look at the full moon, how would the moon look?

A page (with 2 page numbers, front and back) has been torn out of a magazine. The sum of the page numbers on the remaining pages is 525. What is the sum of the page numbers on the page torn out?


Details and Assumptions:

• Each page of the magazine is numbered on both its front and back sides.
• The numbering begins with 1 on the front of the first page and proceeds consecutively in ascending order. The "remaining pages" are the pages before and/or after the page torn out.
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