Problems to Ponder (June edition)

Welcome to this month’s edition of Problems to Ponder! Pose them in your classroom as a challenge, or try them out yourself. Have an interesting student (or teacher) solution? Send it to thevariable@smts.ca for publication in a future issue of The Variable, our monthly periodical.

Why was 6 afraid of 7?
Math Challenge 2016
Put the numbers 1 to 8 in the boxes below so that no consecutive numbers are next to each other (for example, 7 can’t be directly above, below, or beside 6 or 8). Note that consecutive numbers can be diagonal from each other.

Flipping coins
Math Challenge 2016

There are 100 coins on a table.  Each coin is numbered, and they are all arranged heads up.

First, you turn over all of the coins. Then, you turn over only the even numbered coins. Then every third coin, every fourth, every fifth, and so on.  You do this until, on the very last turn, you turn over only the hundredth coin.

When you finish, which coins will be heads up?  Which will be tails up? Explain.

Patchwork

Take a square and draw a straight line right across it. Draw several more lines in any arrangement so that the lines all cross the square, and the square is divided into several regions. The task is to color the regions in such a way that adjacent regions are never colored the same. (Regions having only one point in common are not considered adjacent.) What is the fewest number of different colors you need to color any such arrangement?

Source: Mason, J., Burton, L, & Stacey, K. (1985). Thinking mathematically. Essex, England: Prentice Hall.