### Solution to July's Puzzle: Hiking a Mountain

Last month, you were considering a hiker who walks up a mountain, starting at the bottom exactly at sunrise and reaching the top exactly at sunset. The next day, the hiker walks down the mountain, starting from the top exactly at sunrise and reaching the bottom exactly at sunset, using the same path he used the day before. Assuming that sunrise and sunset times were the same both days, your challenge was how to prove the hiker visited some point along the path at the same time both days.

You can approach this problem a couple of ways. You can think of two different hikers—one going up the mountain and one going down—both starting their hike the same day at sunrise and finishing at sunset. Obviously, they're bound to meet at some point. You can also solve the puzzle graphically, using the X axis to represent the time (from sunrise to sunset) and the Y axis to represent the position (from the bottom of the mountain to the top). Draw two lines representing the position and time of each hike, and you'll have your answer where the two lines meet.

### August's Puzzle: Find the Pattern

Thanks to Erik Veerman of Solid Quality Learning for this month's puzzle: Given the following sequence of integers, identify the pattern in the sequence and how it should continue: 3, 3, 5, 4, 4, 3, 5, 5, 4, 3, 6, 6, 8, 8.