On the campus of

## Green Wall Challenge #1

This first problem comes in two parts, and a bit of mind reading. The parts are different in obvious ways. Solve them both, then read my mind, to do this you may have to ponder for a while the nature of the two parts of the challenge already completed. The winning solution will describe accurately what it is I am aiming for. It isn’t terribly deep, so give it a go in the spirit of fun and joy it is meant. First Problem The Lion, Llama, and Lettuce tri-lemma. There once was a farmer who was taking three items to ...

# Puzzle

### Cups and Downs

This week’s Puzzle Corner activity is a magic trick with a mathematical, as well as a slight-of-hand, component. I first came across this trick in one of Martin Gardner’s many books on recreational mathematics. I liked it so much that I have been stumping students, friends, and family members with it ever since. In order to make… Continue Reading

### The Goalpost Puzzle

The Puzzle Corner activity this week is an adaptation of a classical matchstick puzzle from recreational mathematics. As has been noted before in this column, these puzzles date back to the nineteenth century when matches were first manufactured and began to proliferate. Most matchstick puzzles can be broken into two general categories: those that are geometric in… Continue Reading

### The Infinite I

This week the Puzzle Corner presents an open-ended, spatial-visualization activity that should both challenge and delight your students. The Infinite I is one of those delicious “put-together” puzzles that uses only a few pieces to form hundreds of interesting shapes. In this respect, it is similar to the popular tangram puzzle. Ironically, The Infinite I is a modification of… Continue Reading

### A Touchy Situation

I am indebted to Robert Benjamin, a scientist from the Los Alamos National Laboratory, for A Touchy Situation. Bob first did this activity with his son when his son was in kindergarten. Therefore, he feels that the activity is appropriate for students at all grade levels. He also notes that the activity works best if students use… Continue Reading

### The Fifteen Cent Flip

The Puzzle Corner activity this week comes from the great puzzlist Martin Gardner. In his book Perplexing Puzzles and Tantalizing Teasers, this game appears with the title The Dime-and-Nickel Switcheroo. Six squares are shown forming a two by three rectangle. In every square but one a coin is to be placed three pennies, one dime, and one nickel. The… Continue Reading

### There’s More Than Meets The Eye

This week’s Puzzle Corner activity is a modification of a puzzle that has been around for many years. All the versions of the puzzle I have seen use two identical arcs that are placed one above the other. While the two arcs have the same length, the one on top seems shorter. This illusion persists… Continue Reading

### Fencing Numbers

This week’s Puzzle Corner activity is a simplified version of a game called Fences. The original version has a 10 x 10 dot grid with the digits 0, 1, 2, and 3 spread repeatedly throughout. Each digit represents the number of line segments that will surround that square in a valid solution. For example, a… Continue Reading

### Are All Sides Equal

The object of this puzzle is to place ten pennies (or other small objects) along the sides of the activity sheet so that each side has exactly the same number. There are several different ways that this can be done. After students have found the solution(s) for ten pennies, they record it. They are then… Continue Reading

### Perplexing Pencil Problem

This week’s post introduces a wonderful topological puzzle. Topology is one of the newest fields in mathematics. To illustrate this, note that Henri Poincare’ (1854-1912), who is considered the founder of algebraic topology, published the first systematic treatment of topology in 1895. On the other hand, Euclid (330?-275? BCE), the father of geometry, wrote his… Continue Reading

### Arrow Arrangements

This particular puzzle comes from The Moscow Puzzles. The puzzle is found in the section entitled “Geometry with Matches,” which offers a selection of matchstick puzzles as “geometrical amusements that sharpen your mind.” Arrow Arrangements is one of the more difficult puzzles in this section, and requires students to understand and apply some basic geometric… Continue Reading